Is this correct and if it isn't what is the right answer?

1 5/6

Step-by-step explanation:

We first convert each mixed number to an improper fraction.

To change -6 7/8, we will ignore the negative at first.  Multiply the whole number by the denominator:

6(8) = 48

Add the numerator:

48+7 = 55

Putting the negative back in, we have -55/8.

To change -3 3/4, ignore the negative at first.  Multiply the whole number by the denominator:

3(4) = 12

Add the numerator:

12+3 = 15

Putting the negative back in, we have -15/4.

This gives us

-55/8 ÷ -15/4

To divide fractions, flip the second one and multiply:

-55/8 × -4/15

Multiply straight across:

(-55×-4)/(8×15) = 220/120

Simplifying this, we know that both 220 and 120 are divisible by 10; this gives us

22/12

Both 22 and 12 are even, so they are both divisible by 2.  This gives us

11/6

6 will go into 11 one time, with 5 remaining; this gives us

1 5/6