The easy way requires no algebra, just basic arithmetic.

If the 30 animals had all been ducks, there would have been only 60 legs. The
extra 32 legs were pairs of hind legs belonging to 16 cows.  So there were 16
cows and 30-16 or 14 ducks.

But your teacher probably won't accept that easy way and expects you to use
algebra.

Let c = the number of cows
Let d = the number of ducks

Then 
the number of legs on the cows = 4c
the number of legs on the ducks = 2d

So the system is



Multiply the first equation by -2 to eliminate d
and add the equations term-by-term:

-2c-2d = -60
 4c+2d =  92
------------
 2c    =  32
  c    =  16    <-- so there were 16 cows.

Substitute in c+d = 30

   c+d = 30
  16+d = 30
     d = 14     <-- so there were 14 ducks. 

Edwin