Alright. I have 8 and 9 down with 2 steps. I'm not quite sure if you are required to do 3 steps, but I found solutions in 2. Problem number 6 is an issue in that I had to use a replacement rule to execute the proof, and it was a few more steps than what you are allowed to use. I'll try to hash it out, but I'll go over problem 8 and 9 and how to attack them.
So here is your first problem, complete with step-by step inferences to reach the conclusion with the strategy for attacking proof in general incorporated into it..
Let's approach this from the perspective of the 4 step process.
Step 1 - Look for the single variable.
We do not have it.
Step 2 - Look for a conditional or a disjunction which are most likely to help us start off.
We DO have that. We have two conditionals, but we also have a disjunction. It is usually the case that a proof is constructed by the teacher to set up a constructive dilemma. It is evident in this proof. A constructive dilemma needs two conditionals, a disjunction, and they need to fit the form where the antecedents of both conditionals match both disjuncts of the disjunction. We have this in lines 2, 3, and 4 and we can derive P v T. Go to step 3.
Step 3 - Look for every derivation possible