I having problems figuring out how to work this problem

6X^2+7/3X^2+1 is the answer 3X+6?

Don't know what you mean by "work this"

The way you typed it, there is no useful simplification.
If you meant (6x^2 + 7)/(3x^2 + 1) , there is no useful simplification
After a long division you could state the answer as
2 + 5/(3x^2 + 1) , but certainly not what you have.

(looks like you subtracted part of the numerators with parts of the denominators, it gave me the shivers )