Six Is Nine

"And this is a 6 from somebody's house, or is it a 9? Ya don't know!"

—Moe, trying to solve a mystery, The Simpsons

If you turn the figure 6 upside down, you get a 9, and vice versa. We all know that.

This trope is about those cases where these two numbers becomes a plot point. The most common (but not the only) scenarios:

Causes some sort of confusion in the plot, that doesn't allow it to advance (like the example below).
It's used for The Reveal or a Plot Twist. Often, but not necessarily, is the Number of the Beast.

For example: Alice is a detective and has learned from a phone call that weird things are happening in Apartment 6. She goes over there, investigates, but finds nothing. But the phone calls continue, so Alice goes again to to Apartment 6, only to find out that the apartment where she was investigating was number 9, but the 9 somehow it was unscrewed, and looked like a 6.

WARNING! There are unmarked Spoilers ahead. Beware.

Examples of Six Is Nine include:

General

This is why you'll occasionally see a line beneath these two digits, or their glyphs are otherwise made distinct.

Advertising

Star Trek: Voyager had an ad for its 30th anniversary episode where they showed the number 1966 (Star Trek TOS's first year) and rotated the first 6 into a 9.

Anime and Manga

In The Girl Who Leapt Through Time, the title character notices a '90' tattooed on her arm that wasn't there before. It isn't until she time leaps a few more times that she realizes it was the number of leaps she had left, and it was actually '06.'

Comic Books

In The Broken Ear, Tintin realizes that the license plate "169 MW" is actually "MW 691" flipped upside down.

Film

In National Lampoon's European Vacation, the Grizwolds spend some time with German-speaking relatives. As they leave, they slam the door and the 6 swings down and becomes a 9, they'd been staying with strangers and didn't realize it.
In End of Days, the Number of the Beast is really 999.
Something like that happened in the French/British Film La Grande Vadrouille, set during World War II, with hotel rooms 6 and 9.
In the film version of Minority Report, there was a scene where John Anderton gets Crow's hotel room wrong due to the figure 9 or 6 having a screw loose.
This happens to Lenny in Memento, causing him to bash a random motel resident in the face.

Live-Action TV

In the How I Met Your Mother episode "Bad News", the numbers 50 to 1 are hidden in the episode as a countdown until Marshall receives the news of his father's death. A file folder Barney is holding is marked with the number 9, and later the folder is picked up upside down, now representing the number 6 in the countdown.
In a Halloween episode of Quantum Leap, Sam leaps into the body of a horror writer whose street address is 669. Near the climax, the 9 flips upside down to reveal that the devil is amongst them.
Parodied in an early episode of Saturday Night Live, one sketch was a parody of The Omen. Late in the sketch, one character accuses the child, Damien, of being spawned from Satan, and they should check for the Number of the Beast on his forehead. One character checks by standing behind the child, and declares that everything is okay with him, because the number on his forehead is 999.
Cheers: The bar has a raffle using numbered pingpong balls. Number 99 gets chosen, but Sam points out that the 99 looks like a 66. Hilarity Ensues.
Parodied in 3rd Rock from the Sun:

Harry: "Dick, I've lost all feeling in the left side of my body. [looks at can upside down] Could somebody please call "1-1-6"?

In episode 9 of The Unusuals, the cops find out that the perpetrator of the case they're investigating lives in apartment #6. They go to the apartment, and find the wrong person entirely. Naturally, the apartment they knocked on was actually #9, and the nail had fallen out of the top of the sign. (Cue chase scene, set to "Tunak Tunak Tun", as the actual perp has had plenty of time to prepare to flee...)
In a short sketch on The Benny Hill Show, Benny as a jealous husband breaks into a hotel room and shoots the man & woman in the bed. Then he takes another look at them, looks at the room number, rotates the 6 to a 9, and sheepishly exits.
In an episode of cult The Seventies British cop show The Sweeney, the "6 with a screw missing turns into a 9" gag is used in a scene where a very respectable family are eating dinner when armed policemen crash into their home, and are just as surprised as they are because they were expecting to meet armed criminals. After the mistake is cleared up, the officers leave with apologies and the family calmly return to their meal. Moments later, a crash is heard in the distance, and the father comments that it sounds as though they've found number 9.
In an episode of Diagnosis: Murder a woman found a dead mime in the house she was staying at. She then noticed the 6 in the house number had a nail missing, making it a 9, and she deduced that whoever killed and left the mime got the wrong house. It turns out it was a Red Herring.
Doctor Who:

Rudge: Uh, no. The other way round, I think. You are in cabin 9, and that is where you will find your luggage, Professor.

The Electric Company: A sketch about a lucky number versus an unlucky number.

Newspaper Comics

The Far Side: In one cartoon, a painter has just painted "999" on Satan's office door in hell. Satan doesn't look happy, and the painter says "I must have been holding the dang work order upside down!"
There was a Pearls Before Swine strip where Pig is sitting contently, reading a comic book. Suddenly, The Bluebird of Happiness flies onto his window and announces that he has been watching Pig for years, and thinks he deserves some joy in his life. Pig thanks the bird, who replies "No, thank YOU, Joseph C. Skalabonsky!". It was then revealed that he was supposed to go to 608 Bradbury, but he held the directions upside-down and went to 809 Bradbury, which is Pig's house. The bluebird then says "Ohhhhh.", flies away, and Pig sighs.

Radio

In Old Harry's Game, there is a bit where Satan received a phone call intended for the emergency services because the caller had the phone upside down.

Video Games

Nine Hours, Nine Persons, Nine Doors makes the Number 9 a plot point by having June's bracelet (a 6) actually being a 9, which allows her to open any of the doors in the game, making it an important hint to who Zero actually is.
In the fifth case of Phoenix Wright: Ace Attorney, a piece of evidence contains a note that reads "6-7S 12/2." However, the note was apparently written upside down and it actually reads "2/21 SL-9," tying it to another case altogether.
In Fahrenheit, a timed sequence puts police detectives Carla and Tyler in a hotel attempting to find the protagonist, Lucas, who is hiding in room 369. The player controls Carla/Tyler, but the first "room 369" you enter has someone else inside; the lettering on the door un-sticks and swivels to reveal that they're actually at room 366. The mistake gives Lucas just enough time to get his own objective done and hide.
Pops up every so often in the Professor Layton games. If a puzzle requires you to manipulate a set of numbered tokens which can be freely rotated, it's probably a good idea to assume this trope is in play.

Western Animation

An episode of Rugrats involved Tommy being kidnapped as a result of criminals succumbing to this trope.
Veggie Tales: Larry never got his pizza in one Silly Song because the house number (16) on his door was broken.
When April O'Neil of the 2000s Teenage Mutant Ninja Turtles series was posing as a news reporter, she wore a badge saying she represented channel 9. When it was damaged, it flipped down, making her a reporter for channel 6, referencing the original series. One of several shout-outs in that episode.

Other Media

Comes out many times in riddles like in Riddle 58 here, as seen in the solution.
Episode 4 of Retarded Animal Babies featured a fake TV screen as a bonus feature, and selecting Channel 666 will lead to a video of Satan eating children from a bowl. Channel 999 is this upside down.