(sqrt (8) - sqrt (12) ) / (sqrt (2) - sqrt (3)

Sqrt(8)=sqrt(4 x 2)=2sqrt(2)

Sqrt(12)=sqrt(4 x3) =2sqrt(3)

[2sqrt(2) - 2sqrt(3)] / [sqrt(2) - sqrt(3)] factor out 2 on LHS

2[sqrt(2) - sqrt(3)] /[sqrt(2) - sqrt(3)]

All the sqrts cancel out leaving you with:

**=2**