Expansion of (a+b)^10 will have 11 terms and its r^(th) term is given by
C_r^10 a^r*b^(10-r)
Here a=2x^6 and b=-3/x^2
Hence r^(th) term is C_r^10 (2x^6)^r*(-3/x^2)^(10-r)
= C_r^10 2^r*x^(6r)*(-3)^(10-r)(x^(-2))^(10-r)
= C_r^10 2^r*x^(6r)*(-3)^(10-r)(x^(-20+2r))
= C_r^10 2^r*(-3)^(10-r)*x^(6r-20+2r)
If we have x^28. 6r-20+2r=28 i.e. 8r=48 or r=6 and corresponding term is
C_8^10 2^8*(-3)^2*x^28=(10xx9)/(1xx2)*256*9x^28=103680x^28
and if we have x^(-4). 6r-20+2r=-4 i.e. 8r=16 or r=2 and corresponding term is
C_2^10 2^2*(-3)^8*x^(-4)=(10xx9)/(1xx2)*4*6561x^(-4)=1180980x^(-4)