Which pairs are additive inverses?
a. )
b. -7,7
c.-7,-7
d.7,7
e.6,-6

I was never sure of what the "additive inverse" is. 
So, just now, just for you, I went and looked it up.

The additive inverse of any number ' A ' is the number
that you need to ADD to A to get zero.  That's all !

So now, let's check out the choices:

a), 6, -(-6)

That second number, -(-6), is the same as +6 .
So the two numbers are the same.
Do you get zero when you add them up ?  No.

b). -7, 7
What do you get when you add -7 and 7 ?
You get zero.
So these ARE additive inverses.

c). -7, -7
What do you get when you add -7 to -7 ?
You get -14 .  That's not zero, so these
are NOT additive inverses.

d).  7, 7
What do you get when you add 7 to 7 ?
You get 14.  That's NOT zero, so these
are NOT additive inverses.

e).  6, -6
What do you get when you add 6 to -6 ?
You get zero.
So these ARE additive inverses.

What do we end up with from the list of choices:

a).,  c).,  and d). are NOT additive inverses.

b). and e). ARE additive inverses.

B and E are the corect answers. For a pair of numbers to be additive inverses, that means that the sum of the two numbers must be 0. And only a pair of opposite nunbers, such as 2 and -2, can have a sum of 0.