How do I get the goal $(A \land B) \lor (A \land C)$ from the premises $A \land (B \lor C)$? (Using Fitch) I have 
$$\begin{array}  {r|c:l}
           1. & A \land (B \lor C)
 \\            2. & A \land B
 \\            3. & A          & \land \textsf{ Elim } 2
 \\            4. & B          & \land \textsf{ Elim } 2
 \\            5. & A \land B  & \land \textsf{ Intro } 4, 3
 \\[2ex]\quad 6. & A \land C
 \\            7. & A          & \lor  \textsf{ Elim } 6
 \\            8. & C          & \land \textsf{ Elim } 6
 \\            9. & A \land C  & \land \textsf{ Intro } 8, 7
\end{array}$$
where do I go from here?
How do I get $A \land  B \lor (A \land  C)$
thanks

Hint 1:  If the only assumption you are given is $A \land B$, can you prove the conclusion?  What about only being given $A \land C$?
Hint 2 : Combine the 2 above proofs with 1 more step from the fitch rules.
Long version:  Looking at the last step, 
$$(A \land B) \lor (A \land C)$$
it seems like the final step might be something like $\lor-\textsf{Intro}$.  But using $\lor-\textsf{Intro}$ would require either establishing  $(A \land B)$ or establishing $(A \land C)$, and neither of those follows from the assumption of $A \lor (B \land C)$.
So looking through the fitch rules, most of them create a theorem with a given structure or would require proving something that would be unprovable.  One candidate stands out as what could be the last step of the proof is $\lor-\textsf{Elim}$:
$$\begin{array} {c}
\begin{array} {c|c|c}
         & x & y \\
x \lor y & \vdots & \vdots \\
         & z & z 
\end{array}
\\ \hline
z
\end{array}$$
because one of the assumptions is a $\lor$ type theorem, and the conclusion does follow from either $B$ or from $C$ (in other words, if we had been asked to prove the conclusion from $A \land X$, it would be true whether $X$ was $B$ or $C$).  So build the proof using $x = B$, $y = C$, $z = (A \land B) \lor (A \land C)$ :
$$\begin{array} {r|l|l}
%
(1) & A \land (B \lor C) & \textsf{Assumption} \\
%
\\
%
(2) & A & \land-\textsf{Elim of } 1 \\
%
(3) & B \lor C & \land-\textsf{Elim of } 1 \\
%
\\
%
(4) & B & \textsf{Assumption} \\
%
(5) & \quad A \land B & \land-\textsf{Intro of } 2 ,~ 4 \\
%
(6) & \quad (A \land B) \lor (A \land C) & \lor-\textsf{Intro of } 5 \\
%
\\
%
(7) & C & \textsf{Assumption} \\
%
(8) & \quad A \land C & \land-\textsf{Intro of } 2 ,~ 7 \\
%
(9) & \quad (A \land B) \lor (A \land C) & \lor-\textsf{Intro of } 8 \\
%
\\
%
(10) & (A \land B) \lor (A \land C) & \lor-\textsf{Elim of } 3 ,~ 4 \to 6 ,~ 7 \to 9
%
\end{array}$$
