The prime numbers less than 10 are 2,3,5, and 7.
The 4th digit is the most restrictive. It can only be 2
since the 4 digit number must be even.
Choose the 4th digit 1 way, as 2.
Choose the 1st digit 3 ways, as 3,5, or 7
Choose the 2nd digit 2 ways.
Choose the 3rd digit 1 way.
Answer: 1×3×2×1 = 6 ways.
They are
3572, 3752, 5372, 5732, 7352, 7532.
Edwin