You have (B v C) in step 3. If you reread the section on the V-elimination rule, it says something like "from (P v Q), a subproof which starts with P and ends with Z, and a subproof which starts with Q and ends with Z, we can infer Z." (I've only scanned that text, but it more-or-less says that, I think). So, if you can do so, it would work out well to start with B and show that it leads to ((A∧B)∨(A∧C)), then you'd start with C and show that it leads to ((A∧B)∨(A∧C)). Now, you have A from step 2 validly inferred by ^ elimination. So, if you have A, and you've assumed B, what can you infer under the scope of assumption B? Then note what the conclusion comes as. It consists of a disjunction. What rule do you have for getting to a disjunction? In other words, what rule do you have for inferring to a disjunction? Do you have "half of" that disjunction (in other words... do you have either the first or the second disjunct?)? If you have A, and you've assumed C, what can you infer under the scope of assumption C? Can you link this with the conclusion also?
Does that help enough?
