Hi mukherjee.tanuj3,

This DS question is based on triangle rules (and whether they apply or not).

**It's important to note that in a DS question, you cannot "trust" the picture (it's not necessarily drawn to scale). Here, it looks like triangle ABD is the same size as triangle ACD, but we CANNOT ASSUME THAT.**

The question asks us for the area of triangle ABC, so we need the height (AD) and the base (BD + CD) to answer this question. The prompt gives us the height, so we need to know BD and CD to answer this question.

Fact 1: Angle ABD = 60

This tells us that triangle ABD is a 30/60/90 triangle; with the height (given), we can figure out the length of BD. HOWEVER, we DO NOT know what type of right triangle ACD is - it could be 30/60/90 or 45/45/90 or neither, so there's no way to figure out the length of CD.
Fact 1 is INSUFFICIENT

Fact 2: AC = 12

This gives us 2 sides of triangle ACD, so we can figure out CD. However, with triangle ACD, we run into the same problem as in Fact 1 above - we don't know what type of right triangle we're dealing with, so we can't figure out BD.
Fact 2 is INSUFFICIENT

Combined, we have the height (given) and the two parts of the base, so we can answer the question.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich