A few things to note first:

2 even numbers multiply to give an even number.

1 odd number and one even number multiply to give an even number.

In other words, for a product to be even, at least one of the factors has to be even!

Consider

WE know the LHS if even because 2 is even. And any number times an even number is even!

So we know the RHS must also be even.

And if a product is to be even, at least one of the factors has to be even. So either (k+1) or (k-1) or both is even.