How many positive four digit even numbers can be written without using 0,1,2,3,4?

Permitted digits: 5, 6, 7, 8, 9. Even numbers must end in 6 or 8. That’s a choice of 2 digits out 5.

If no repeated digits are allowed, and the 4-digit number ends in 6, then we need to choose 3 out of the remains 4 digits. There are 4 possible choices and 6 ways of arranging each combination. So for even numbers ending in 6 there are 24 numbers with no repeated digits. Similarly there are 24 even numbers ending in 8, making a total of 48 4-digit numbers.