Find an element of order 4 in the alternating group A6? Does A6 have an element of order 6?

Attempt

A6 has 6!/2 elements=360

Prime factorization of this is 2^3*3^2*5

Therefore it has elements of order 8, 9 and 5, so no element of order 6?

but this means i cant do the first part

Some insight would be great

Thanks in advance

Niall