Question 315902
Let's do a simpler problem first. You have 3 shirts (Red, Green, Yellow) and 2 pants (Blue, White). How many outfits can you make? 

Let's say you choose Red shirt. Then your outfits are RB and RW. 
Let's say you choose Green shirt. Then your outfits are GB and GW. 
Let's say you choose Yellow shirt. Then your outfits are YB and YW. 

So there are three shirts you could have chosen, and for each of them, you have 2 pants to choose from. The total number of outfits is 2 + 2 + 2, or you could have done 2*3 to get 6. 

In general, the same principle holds true. You just multiply the different possibilities to get the total number. 

So 4 appetizers, 9 entrees, 3 desserts and 12 drinks make 4*9*3*12 = 1296 different meals.