Answer
The function is not one to one.
Work Step by Step
Notice that the graph of this function does not pass the horizontal line test, because it is possible to draw a horizontal line that passes through the graph more than once, as shown in red. This means the function is not one-to-one.
$-3((6\sqrt{\frac{8}{3}})-6)^2+8=0=-3((6\sqrt{\frac{8}{3}})-6)^2+8$
Equivalently, notice that it is possible to find two different $x$ values that have the same $y$ value ($x=6+\sqrt{\frac{8}{3}}$ and $x=6+\sqrt{\frac{8}{3}}$ both have $y$ value 0). This means the function is not one-to-one.
