$L = \{ w: |w| \bmod 3 \geq |w| \bmod 2 \}$
I know, when the length of strings is not $3, 9, 15, 21,\dots,$ they will be members of the given language but unable to write a grammar for this language.
Please confirm one more thing, that this given language is regular?
Note that this language excludes all strings of length divisible by 3 but not by 2, i.e., of length $3, 9, 15, 21,\dots$.
Consider languages $$L_1 = \{w\mid |w|=2k, k\geq 0\}$$ and $$L_2 = \{w\mid |w|=3k, k\geq 0\}$$ They are regular, since it is very easy to design DFA for both languages; the first has three states, the second has four states. The complement of the language $L$ is equal to $L_2-L_1$, and by the closure properties of regular languages $L=\overline{L_2-L_1}$ is also regular.
