Algebra method is presented (usually applicable only for upper primary students).

Alternatively, you can use the trial and error method, e.g.
assume 30 pigs and 28 chickens (total must be 58),
Total number of legs = 30 x 4 + 28 x 2 = 176
Opps, too high. Number of pigs should decrease since pigs have more legs. Let's try 20 pigs and 33 chickens.
Total number of legs = 20 x 4 + 33 x 2 = 146.
Too low. Increase number of pigs so that total legs can increase. You continue this process until you get to 34 chickens and 24 pigs.