Let L be context free language lets take L = {$a^{n}b^{n} | n > 1$}
Let M be regular language, lets take L = { $a^{*}b^{*}$ }
L ⋂ M = {$a^{n}b^{n} | n > 1$} which is CFL
Only case i can think of regular is when you get $\phi$ as intersection, anyhow all regular language is CFL by default.
So we can say answer should be always CFL which is option D.