Answer
$$331,776$$
Work Step by Step
Step 1:
Substitute $x=-3$, $y=4$ and $z=6$
$(2xy^{2}z)^{2}$
$(2*-3*4^{2}*6)^{2}$
Step 2:
Remember the order of operations
Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction
So first,
Since we do not have any parenthesis, we do exponents.
So,
$(2*-3*16*6)^{2}$
Step 3
Multiplication
$(-576)^{2}$
Step 4
Finish the last exponent
$331,776$