Here is a derivation of A and B in Fitch-style natural deduction.

Code:

0 ~G /\ A Given
1 A 1 Conjunction elimination
2 ~B Assumption
3 ~B => ~A Given
4 ~A 2, 3 Modus Ponens
5 False 1, 4 Negation elimination
6 ~~B 2, 5 Negation introduction
7 B 6 Double-negation elimination

~G is derived from the given ~G /\ A in one step using conjunction elimination.

I have to apply propositional logic based inference rules

I have already said in post #4 that there are many sets of inference rules for propositional logic, and some of them look very different from each other. The only way to find out which rules you need to use is to go back to your textbook/lecture notes or ask your instructor. Mathematics starts by positing precise definitions of objects it studies (in this case, inference rules). Without definitions, there is no math.