Answer
$-101,376$
Work Step by Step
According to Binomial Theorem, the term containing $x^k$ in the expansion of $(x+p)^n$ can be determined as:
$\displaystyle{n}\choose{n-k}$$ p^{n-k}x^k (1)$
Using formula (1), replacing $x$ with $2x$ and $c$ with $-1$, the term containing $x^7$ in the expansion of $(2x-1)^{12}$ can be written as:
$\displaystyle{12}\choose{12-7}$ $(-1)^{12-7}(2x)^7 =$$\\\displaystyle{12}\choose{5}$ $(-1)^{5}(2x)^7 \\=\displaystyle\dfrac{12!}{5!7!} (-1)(128x^7)
\\=(792) (-128x^7)
\\=-101,376x^7$
Therefore, the coefficient of the term that contains $x^7$ is: $-101,376$
