Two ways to do it: with and without algebra:

Without algbra:

Since there are 172 eyes, there are 86 animals. If they were all cows there 
would also be 86x4 = 344 legs. And that's how many there are, So they are all
cows.  86 cows and no birds.  

So the problem is wrong for stating that he has some birds.  I suppose the trick
is that 0 birds is a number of birds, since 0 is a number.

In that case I own a number of gold mines, yachts, mansions, and Ferraris.
That's because I have won the lottery a number of times. Hahaha J

With algebra:

2c + 2b = 172
4c + 2b = 344

Subtract the first equation from the second and get

     2c = 172
      c = 86

Substituting in the first:

   2c + 2b = 172
2(86) + 2b = 172
  172 + 2b = 172
        2b = 0
         b = 0

Edwin