It sure is not easy to extract information from you Which book are you using? (I am interested to know anyway, but I won't be able to consult it to see the description of the proof system unless it is online.) Also, you have not said if you understand disjunction elimination, which is important in this example.

Here is my best guess about the complete derivation.

Code:

1| C ∨ ~B ASS
2|| C ASS/∨E
3|| A ⊃ (B ∧ ~C) ASS
4||| A ASS/~I
5||| B ∧ ~C 4,3⊃E
6||| ~C 5∧E
7|| ~A 4,2,6~I
8|| ~B ASS/∨E
9|| A ⊃ (B ∧ ~C) ASS
10||| A ASS/~I
11||| B ∧ ~C 10,11⊃E
12||| B 11∧E
13|| ~A 10,12,8~I
14| ~A 1,2,7,8,13∨E
15| C ∨ ~A 14∨I

I prefer a tree presentation of the derivation. Here closed assumptions are labeled with step numbers in the derivation above where these assumptions are introduced. Similarly, rules that close assumptions (~I and ∨E) are labeled with the assumptions' numbers.