Answer
See work below.
Work Step by Step
The values of $m_{\mathcal{l}}$ range from $-\mathcal{l}$ to $\mathcal{l}$, or $2\mathcal{l}+1$ values. For each of those electrons, $L_z=m_{\mathcal{l}}\hbar$. Adding up the z-components of the orbital angular momentum gives a sum of zero, because the positive components cancel the negative components.
Half of the electrons are “spin up” and the other half are “spin down” so the spin angular momentum also sums to zero.
We see that the total angular momentum of the filled subshell is zero.
