Unless I'm misunderstanding you, that's what I've done. If you don't mind I'll go through my reasoning (forgive me if I use incorrect terminology in places, I'm new to this!), because I'm not sure if I'm doing this wrong.
The conclusion is a conjunction, which I've made False. As the conjuncts are ~A and F, I have made F true, A false, but the negation true.
To make the conditional in the first premise true, I have made B false, since A is true. This makes the negation in the second premise true, so I have made C in the second premise true, to make the whole premise true.
This makes the disjunctive in the third premise true, as C is true and I don't need the truth value of D, since if either disjunct is true then so is the whole statement. I then made E true, to make the entire statement true.
If E is true, I only need to make F true to make the fourth premise true. So now all four premises are true, and the conclusion is false.... I think....