Question 9f3afe4b

$f\left(x\right)=(x-1)(x+3)(x-2)$

In the xy-plane, when the graph of the function $f$, where $y=f\left(x\right)$, is shifted up $6$ units, the resulting graph is defined by the function $g$. If the graph of $y=g\left(x\right)$ crosses through the point $\left(4,b\right)$, where $b$ is a constant, what is the value of $b$?