If an atom has an electron in the n = 4 state with ml = 2, what are the possible values of l?

The possible values of l are 2 and 3

Explanation:

Each electrons have four quantum numbers:

n: the principal quantum number, which value matches with the energy level of the electron. l: the secondary quantum number, which value can be from 0 to n-1m: the magnetic number, which value can be from -l to l sp: the spin number which value can be -1/2 or +1/2

In this case, n=4 so the values of l are:

l=0, 1, 2, 3

Now, if:

l=0 the value of m is m=0l=1 the values of m are m= -1, 0, 1l=2 the values of m are m= -2, -1, 0, 1, 2l=3 the values of m are m= -3, -2, -1, 0, 1, 2, 3

Being all that said, l can be either  equal to 2 or 3