Given that $(2x+4)^{10}$
Directly we can apply the Binomial theorem
$(a+b)^{n}=\sum_{k=0}^{n}\binom{n}{k}(a)^{n-k}\cdot(b)^{k}$
Now$,(2x+4)^{10} =\sum_{k=0}^{10}\binom{10}{k}(2x)^{10-k}\cdot(4)^{k}$
We want coefficient of $x^{7},$so we can put $k=3$ and we get $x^{7},$
$\Rightarrow\binom{10}{3}(2x)^{10-3}\cdot(4)^{3}$
$\Rightarrow\binom{10}{3}(2x)^{7}\cdot(4)^{3}$
$\Rightarrow\binom{10}{3}(2)^{7}\cdot x^{7}\cdot(4)^{3}$
So,Coefficient of $x^{7}$ is $:\binom{10}{3}(2)^{7}\cdot(4)^{3}$
$\Rightarrow120\cdot128\cdot64$
$\Rightarrow983,040$
So,correct answer is$:983,040$