Consider the following premises. exists x_12: Q_3(x_12) and Q_6(x_12). forall x_12: P_12(x_12) and Q_12(x_12). Can we infer exists x_12: Q_3(x_12) and P_12(x_12) from them?
 From forall x_12: P_12(x_12) and Q_12(x_12) we can infer forall x_12: P_12(x_12). From exists x_12: Q_3(x_12) and Q_6(x_12) we can infer exists x_12: Q_3(x_12). Finally, from exists x_12: Q_3(x_12), forall x_12: P_12(x_12) we can infer exists x_12: Q_3(x_12) and P_12(x_12). Therefore, the answer is yes.