Consider the following premises. q_6 -> w. q_4 -> q_6. ~w. w -> q_6. Can we infer q_4 from them?
 From w -> q_6, q_6 -> w we can infer w <-> q_6. From w <-> q_6, ~w we can infer ~q_6. Finally, from q_4 -> q_6, ~q_6 we can infer ~q_4, which contradicts q_4. Therefore, the answer is no.