Solve the triangle.
A = 19°, C = 102°, c = 6
choices are
B = 31°, a ≈ 18, b ≈ 15.8
B = 59°, a ≈ 2, b ≈ 5.3
B = 59°, a ≈ 18, b ≈ 15.8
B = 59°, a ≈ 18, b ≈ 5.3
The problem as stated can be solved without using the laws of sines or cosines, if I'm right that capital letters stand for angle measures and lower-case letters stand for lengths of sides, and c (for example) is the side opposite C. That would be a common convention.
19+102= 121 and 180-121=59. This eliminates your first choice.
The longest side will be opposite your largest angle. Since C is the largest angle, c=6 is the longest side. That eliminates the third and fourth choices, leaving only the second.
You could check out the second choice using the sine law if you want.