The best way to learn how to do word problems is to practice
by looking up the answer to the word problem in the back of 
the book and then checking it in the words to see why it is
the correct answer.  

That's because the logic required to check a word problem when 
you DO know the answer, is exactly the same logic that you use 
to set up the word problem when you DON'T know the answer. You 
simply "check" the problem using an unknown instead of a known.

So first I'll tell you the answer in advance.  Then we'll check 
it. Then I'll tell you how to get it. 
Bear with me.

The answer is: Peter is 26.  

Let's check that first:

Peter is 26 years old, and is 12 years older than Mario, who is therefore 12
years less, or 14. Mario's age 2 years from now will be 14+2, or 16, and 
that equals half of Peter's age 6 years from now, for since Peter is 26 now,
he will be 32 then, and indeed 16 equals half of 32.

Now let's "check" it using the unknown P instead of the known 26, using
the exact same words:

Peter is P years old, and is 12 years older than Mario, who is therefore 12
years less, or P-12. Mario's age 2 years from now will be (P-12)+2 or P-10, and
that equals half of Peter's age 6 years from now, for since Peter is P now, 
he will be P+6 then, and indeed P-10 equals half of P+6.

Those last words, "P-10 equals half of P+6", tells us that our equation is:

P-10 = (P+6).

Solve that and get P = 26, and then Mario is, of course, 12 years younger or
14.

Edwin