the question is asking to form a 4-digit number. i think the answer should be 60.

In the qn,it is not mentioned that number repetition is allowed or not so:
with repetition:
thousandth place can be filled in 4 ways as 0 is not possible
hundredth place can be filled in 5 ways
tenth place can be filled in 5 ways
unit place can be filled in 3 ways(0,2,4) == 4*5*5*3 ->300 ways

without repetition:
thousandth place can be filled in 4 ways as 0 is not possible
unit place can be filled in 3 ways(0,2,4)
hundredth place can be filled in 3 ways
tenth place can be filled in 2 ways
== 4*3*2*3 ->72 ways


Is this correct?

Judging from the official answer, it looks like the question was intended to have no repetition.
The problem with your solution here is that, if the first (thousands) digit is 4 or 2, then there aren't 3 ways in which the units digit can be chosen.
I would probably break the solution into two cases:

case 1: the units digit is 2 or 4.
Here, there are 2 options for the units digit.
There are 3 options for the thousands digit (anything but 0 or the even digit chosen for the units digit)
There are 3 remaining options for hundreds digit
And 2 remaining options for tens digit
Total = 2 x 3 x 3 x 2 = 36

case 2: the units digit is 0.
Here, there 1 option for the units digit.
There are 4 options for the thousands digit (anything but 0)
There are 3 remaining options for hundreds digit
And 2 remaining options for tens digit
Total = 1 x 4 x 3 x 2 = 24

Answer = 36 + 24 = 60

Fixed. Thank you