(x^2y^6-3)^2 .....PLEASE HELP ME I HAVE NO IDEA HOW TO SOLVE THIS IVE BEEN DOING IT FOR HOURS
Do you mean multiply it out? You can not "solve" something that is not an equation.
To multiply, use the distributive property :
x^2y^6 (x^2y^6-3)-3(x^2y^6-3)
x^4 y^12 - 3 x^2y^6 -3 x^2y^6 + 9
x^4y^12 -6 x^2y^6 + 9