Note that Monday is dry so the first two branches are dry (0.8) and rainy (0.2). Now draw the next set of branches and use the given information to label their probability.
Now use the tree diagram to get the answer. I get (0.8)(0.2) + (0.2)(0.6) = .... but you better double check because I'm terrible at these things.
Let p denote the probability of dry/rainy
Mon Dry: p=1
Tue Dry: p=0.8
Wed Dry: p=0.8*0.8
Wed Rainy: p=0.8*0.2
Tue Rainy: p=0.2
Wed Dry: p=0.2*0.4
Wed Rainy: p=0.2*0.6
hence simply add up all the probabilities that makes Wed a rainy day