Answer
$\mu_{orb,z} = -3~\mu_B$
Work Step by Step
For each $l$, the values of $m_l$ can be $~~m_l = 0, \pm 1, \pm 2,...,\pm l$
When $l=3,$ the largest possible value of $m_l$ is $~~m_l = 3$
We can find an expression for $\mu_{orb,z}$:
$\mu_{orb,z} = -m_l~\mu_B$
$\mu_{orb,z} = -3~\mu_B$
