The given answer is incorrect.

To be even the string must end in 2 or 4.

The string can be arranged in ways.

Add a 2 to the right-hand end of each of those 30 strings.

That is is an even number.

Now swap the 4 and the 2 from each of above that gives another 30.

So 60 in all.

BTW: there are 120 odd numbers.