Answer
There are 2 available states with the greatest $m_l$ value.
Work Step by Step
$l=3$
In general, the allowed values of $m_l$ are $~~m_l = 0, \pm 1, \pm 2,...,\pm l$
If $l=3,$ then the allowed values of $m_l$ are $~~m_l = 0, \pm 1, \pm 2, \pm 3$
The greatest $m_l$ value is $~~3$
For each value of $m_l$, there are 2 possible values of $m_s$
There are 2 available states with the greatest $m_l$ value.
