I like to teach my students that the Distributive Property is just like going to a party. Here's how it works. You have an expression like 3(x+4) and you want to simplify it. (FYI: Simplify means "get rid of the parenthesis"). OK, the party is what is going on inside the parenthesis. In this problem, (x+4), and the guests are x and 4. The number 3 is outside of the party, but knocking at the door to come in. When 3 enters the party, it is only polite to greet ALL the guests, right? Greeting = multiplication. So, 3 comes in and greets x (giving us 3x) and 3 greets 4 (giving us 12), so the expression simplifies to 3x+12.

(This idea is from Danika McKeller's "Kiss My Math")