find the term independent of x in the expansion of (2+x^2)^6 (1-3/x^2)^2
so you want the terms that contain x^0
In (2+x^2)^6 (1-3/x^2)^2
we have the following:
= (2^6 + 6(2^5)x^2 + 15(2^4)x^4 + ...)(1 + 2(-3/x^2) + 9/x^4)
so we only have to worry about:
2^6 (1) , 6(2^5)x^2 * (-6/x^2) and 15(2^4)x^4 * 9/x^4
their sum is
64 + (-1152) + 2160
= 1072