Answer
$f(3) \gt 6$
Work Step by Step
Let's assume that $f(3) \leq 6$
Since it is given in the question that $f(3) \neq 6$, then $f(3) \lt 6$
It is given that $f(2) = 8$
Note that $f(3) \lt 6 \lt f(2)$
Since $f$ is continuous on the interval $[1,5]$, there must be a number $c$ where $2 \lt c \lt 3$ such that $f(c) = 6$
However this contradicts the statement that $x=1$ and $x=4$ are the only solutions of the equation $f(x) = 6$
Therefore, our assumption must be false. Thus, $f(3) \gt 6$
