what i did here was set n = 3 that makes the whole expression as 224 a even number after that i pluged 224 into the another equation that makes first two terms positive and the last one negitive and got the answer as one. where did i go wrong?

You don’t plug 224 (which is the value of n^5 - 4n - 7 when n = 3), you plug 3. The question asks you to find a value in terms of n.