By the binomial theorem, which says
[tex](a+b)^n=\displaystyle\sum_{k=0}^n\binom nka^{n-k}b^k[/tex]
where [tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex], the seventh term of the expansion is given when [tex]k=6[/tex]. Take [tex]n=11[/tex], [tex]a=4x[/tex], and [tex]b=-2y[/tex], and we get
[tex]\dbinom{11}6(4x)^{11-6}(-2y)^6=462\cdot4^5x^5\cdot(-2)^6y^6=7569408x^5y^6[/tex]
Note: it's possible that you may know the binomial theorem in the reverse direction, which says
[tex](a+b)^n=\displaystyle\sum_{k=0}^n\dbinom nka^kb^{n-k}[/tex]
in which case the answer would be [tex]-60555264 x^6 y^5[/tex].
