Answer
$L_z = 3.16\times 10^{-34}~J~s$
Work Step by Step
For any given value of $l$, the values of $m_l$ can be $~~m_l = 0, \pm 1, \pm 2,...,\pm l$
When $l = 3$, the largest value of $m_l$ is $~~m_l = 3$
We can find the magnitude of the largest projection on an imposed z axis:
$L_z = m_l~\hbar$
$L_z = 3~\hbar$
$L_z = \frac{3~h}{2\pi}$
$L_z = \frac{(3)~(6.626\times 10^{-34}~J~s)}{2\pi}$
$L_z = 3.16\times 10^{-34}~J~s$
