Start by writing all elements of S_4. To be more precise A_4 is a subgroup of S_4 not only a set.

Generally if you want to find elements in S_n then consider all the partations of n, i.e., all the different methods n can be written as sum of positive integers.

Here we have that 4 = 4, 4=3+1, 4=2+2, 4=1+1+2, 4=1+1+1+1. These are the only elements of S_4.

SO in cycle form we write:

Cycle number of elments of this cycle type

(*)(*)(*)(*) 1

(**)(**) 3

(*)(***) 8

(*)(*)(**) 6

(****) 6

It can be little bit difficult for you to find number of elements of a given cycle type because you need some combinatoirs for that, but you will get use to it.

A permutation is even if it can be written as a product of even number of permutations.

I hope this helps, otherwise write again.