In how many ways can 4 people sit next to each other in a movie theater row?

The first seat can be any one of the 4 people.
For each of those . . .

The second seat can be any one of the remaining 3 people. 
For each of those . . .

The third seat can be either one of the remaining 2 people. 
For each of those . . .

The fourth seat is the last remaining person.

Total number of possible ways to line them up = (4 x 3 x 2 x 1) = 24 ways.