you have to "accumulate" (multiply) the probabilities along the path (Pinit * Pemit_1 + Ptransition_1_to_2 * Pemit_2 * Ptransition_2_to_3 * Pemit_3 *....), taking the max at each step.
In your case:
Q2 : 0.8 * 0.2 * 0.1 * 0.2 = .0032 (no max to take here since no ambiguity)
Q3 : 0.8 * 0.2 * max(0.9 * 0.1 * 0.5 , 0.1 * 0.2 * 0.4) * 0.3 = 0.8 * 0.2 * 0.9 * 0.1 * 0.5 * 0.3 = 0.00216
In your case:
Q2 : 0.8 * 0.2 * 0.1 * 0.2 = .0032 (no max to take here since no ambiguity)
Q3 : 0.8 * 0.2 * max(0.9 * 0.1 * 0.5 , 0.1 * 0.2 * 0.4) * 0.3 = 0.8 * 0.2 * 0.9 * 0.1 * 0.5 * 0.3 = 0.00216
