Independent Random Variables - Variance of 2 Die

Hi, can't seem to figure this one out. Can someone tell me where I'm going wrong?

Two fair dice are tossed together. Let X be the sum and Z be the average of the 2 numbers that show on top. Find V(X-Z).

I found V(X) = (35/12)(2) = 35/6

Was is correct to multiply (35/12) by 2? to account for there being 2 die?

And as for V(Z), I believe the E(X) is 3.5 but I'm not sure how to calculate the rest of the variance. I get 35/12..which gives me the wrong answer.

The answer at the back is 35/24.

Thanks!