If n represents an even number, which expression represents the product of the next two even numbers

a. n^2 + 3n + 2
b. 2n + 3
c. 2n + 6
d. n^2 + 6n + 8

I'm completely stuck here, so please explain how you got the answer? :) Thank you so much :) <3

Think about it, the next even number would be 2 after n because every other number is even. The next even number would be 4 after n. The product of them would be (n+2)(n+4) which equals n^2 +6n +8
so d is your answer

a is wrong n^2 + 2n + n + 2 = n ( n+2 ) + n + 2 = ( n+2 ) ( n+1 ) two consecutive numbers can't be both even
b is wrong 2n + 3 = ( n+1 ) + ( n+2 ) two consecutive numbers can't be both even
c is wrong 2n + 6 = ( n+3 ) + ( n+3 ) an even number + 3 isn't even

so the only one remaining is d that is correct n^2 + 4n + 2n + 8 = n ( n+4 ) + 2 ( n+4 ) =( n+4 )( n+2 )
2 even numbers

If n represents an even number,
which expression represents
the product of the next two even numbers?
(n + 2)(n + 4)
Answer:
d. n^2 + 6n + 8

(n + 2)(n + 4) = n^2 + 6n + 8

Why? = n, n + 2, n + 4, n + 6 and so on is the series of even numbers from n on.