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OK, let's check this thing with some real numbers...  Just so we can really believe that it works.

2 ( 3 + 4 )

First, let's do it the official "order of operations" way...  Hit inside those parenthesis first!

2 ( 3 + 4 ) = 2 ( 7 ) = 14

Now, let's use the distributive property:

2 ( 3 + 4 )
We distribute the 2 to the 3...  and, then, to the 4...
Remember the order of operations after that! 
Multiplication, then addition!

2 ( 3 + 4 ) = 2 ( 3 ) + 2 ( 4 ) = 6 + 8 = 14

Yep!  We got 14 again.  So, it works!

Go ahead and try it yourself with any three numbers.  It will always work.