Presumably [B] and [D] have been marked off as incorrect. That leaves us with [A] and [C].
The solid lines represents the "or equal to" line, (<= or >=), while the dotted line just represents "not equal to" (< or >).
Pick any point inside of the feasible region. I'm going to pick (5, -5). Slot the values in to an equation, and if it ends up true, then that's the equation you're looking for, otherwise, it's likely the other one.
2(5) + 3(-5) <= 5
10 + -15 <= 5
-5 <= 5
TRUE
From this answer alone, I pretty much know the answer is [A], as [C] has the same inequalities, but they are inverse. Though, I'll prove to you the other equation of part [A] as well.
-3(5) + 2(-5) < 6
-15 + -10 < 6
-25 < 6
TRUE