Answer
$7,838,208\sqrt2u^{5}$
Work Step by Step
The $r+1$ th term in the binomial expansion of $(x+y)^n$ is:
$\binom{n}{r}x^{n-r}y^r$
Here $x=2u$, $y=3\sqrt{2}$, $n=10$:
There are 11 terms in this expansion, the middle one is the 6th.
$r+1=6$
$r=5$
The indicated term is:
$\binom{10}{5}(2u)^{10-5}(3\sqrt{2})^5=252\times2^5\times u^{5}\times 972\sqrt2=7,838,208\sqrt2u^{5}$