The third way you mention to fill the Ls, the two blocks stacked on top of each other, are "lying flat" setups. Don't count them twice.
Still trying to work out the rest of your post.
Edit: Okay,
If you divide the blocks into two Ls as you said, there are 3 distinct, asymmetrical ways to position them.
Taking rotation into consideration, that's still only 6 possibilities. Once you place one block in the L, the other block only has one place to go. P(3,2) = 6.
+2 for the possibilty that the four blocks don't fill the assumed Ls, so the answer is 8.
Thanks for the justification on E.
Still trying to work out the rest of your post.
Edit: Okay,
If you divide the blocks into two Ls as you said, there are 3 distinct, asymmetrical ways to position them.
Taking rotation into consideration, that's still only 6 possibilities. Once you place one block in the L, the other block only has one place to go. P(3,2) = 6.
+2 for the possibilty that the four blocks don't fill the assumed Ls, so the answer is 8.
Thanks for the justification on E.