There are four quantum numbers in an electron that orbits the atom.
n is a positive integer. The value of n indicates the main shell of the electron. The electron in question is in the 3s orbital. As a result, n = 3.
l is a non-negative integer. The value of l indicates the type of subshell ("orbital") of the electron. The types of subshells possible depends on the main shell. For example, both s and p orbitals exist in the second main shell. However, only the s orbital exists in the first main shell. The value of l ranges from 0 to n - 1.
The electron in question is in an s orbital. As a result, l = 0.
[tex]m_l[/tex] is an integer. The value of [tex]m_l[/tex] indicates the position of the electron within the subshell. The range of [tex]m_l[/tex] depends on the value of l. [tex]m_l[/tex] ranges from -l to l (that's -l, ..., -1, 0, 1, ... l). Accordingly, there are 2 l + 1 orbitals in a l subshell. l = 0 for this 3s electron. There's only one orbital in the 3s subshell. The only [tex]m_l[/tex] value possible for this electron is 0.
The value of [tex]m_s[/tex] is either - 1/2 or 1/2. It indicates the position of an electron within a single orbital. The value of [tex]m_s[/tex] does not depend on that of n, l, or [tex]m_l[/tex]. However, by the Pauli Exclusion Principle, at least one of the four numbers must differ for two electrons in the same atom. In case all three of n, l, and [tex]m_l[/tex] are the same, the two electrons must differ in [tex]m_s[/tex]. However, this question asks only for the number of one single electron. Thus, giving either - 1/2 or 1/2 shall work.
Vitz et. al, "5.8 Quantum Numbers (Electronic)", ChemPRIME (Moore et al.), Chemistry Libretexts. 27 Oct 2017.
