If I understand you correctly, you are being asked to prove that the sentence
[(P → Q) → (P → R)] → [P → (Q → R)]
is a tautology, or a valid sentence of propositional logic. I'm also assuming your conditional should be represented as the material conditional, since this is the one you are most likely using in an introductory course on logic. I've replaced your "if/then" with →.
A good rule of thumb when being asked to prove a conditional is to work backwards from the conclusion. Treat the antecedent of the conditional as an assumption, then prove the consequent part, so that your final step is discharging that assumption by the rule of conditional proof. So you want to assume (P → Q) → (P → R) and prove P → (Q → R). Since P → (Q → R) is also a conditional, do the same thing with that: assume P, prove Q → R then discharge the assumption using conditional proof. Since Q → R is also a conditional, do the same thing again: assume Q and prove R. Put together it looks like this:
1. (P → Q) → (P → R) Ass.
2. P Ass.
3. Q Ass.
4. P → Q 3, Impl.
5. P → R 1,4 MP
6. R 5,2 MP
7. Q → R 6,3 CP
8. P → (Q → R) 7,2 CP
9. [(P → Q) → (P → R)] -> [P → (Q → R)] 8,1 CP
At step 4, I've assumed that you have a rule for material implication that allows you to go from Q to P → Q. If you are not allowed this rule, then you will need an extra step to prove that.