Hi,
Let's go on with the statements:
1) Two of the sides measure 6 long and 2 of them measure 8 long:
This one alone could be a rectangle or a trapezoid or still a quadrilateral with two equal sides adjacent.((not sufficient))

2) the diagonals are perpendicular to each other:
This one alone could be a square(some sort of rectangle then) or a rhombus.(not sufficient)

Now let's consider both of them together:
If the sides are not equal according to part one, then it could not be a square described in part two. And because the diagonals are perpendicular to each other, it should be an unknown quadrilateral which the pairs of equal sides, appear adjacent. The only rectangle with perpendicular diagonals is a square. So the answer is No regarding both statements together.(sufficient)

Always be aware of these No answers, they sometimes try to deliver unconsciously a non-sufficient answer.
I hope it can help
bests

So are you saying it is a rhombus after looking at both A & B and not a rectangle?

I would pick C as the answer if I saw this on the exam, but I would think it was a rectangle.

Thanks Anurag.