Which pair of triangles is congruent by ASA?

This is simple. I actually explained something similar to this 5 minutes ago, but I'll do it again XD. 

In terms of congruency, you have about 8 different ways, I only remember 4.
SSS (Side, Side, Side)
SAS (Side, Angle, Side)
ASA (Angle, Side, Side)
AAA (Angle, Angle, Angle)

Now, those little marks on those triangles are important. They show you what's congruent! 
The symbols mean that side or angle is congruent to any side or angle that has the SAME symbol, respectively. 

ASA means there will be 2 sets of angles identified via symbols as congruent, and 1 set of sides, also via symbols, but what sides or angles claim to be congruent MUST ACTUALLY BE CONGRUENT, they turn the shapes different ways to confuse you, don't let that mess you up.

Set A of triangles: the TOP angles are identified as equal via the half-cirlce, and both are indeed congruent. However, the DOUBLE half circle marks are on opposite sides of the triangle, AND the dash for the sides are on different sides of the triangle. This is wrong.

Set B of triangles show the TOP angles are congruent, identified by the half circle, and these are indeed correct. Now, this is where it gets tricky: At first glance, if you simply rotate the shape, it won't look congruent, because the side and the double lined angle are opposite. However, they ARE indeed congruent, the shape was simply mirrored. You can also tell because these are even triangles, the bottom angles and the two side-angles are naturally congruent. 

Set C AND D of triangles are all correct, however these are SAS, not ASA.

Your answer is the second set of triangles, B
~Hope this helps!