Angle ADB = 180 - 2x
Angle ABD = 180 - (x + 180-2x)
Angle DBC = 180 - 4x

All the angle relationships are known with respect to X.

A triangle can have infinite dimensions which would still keep the angles consistent.

Statement 1 says AD=6
If all the angle relationships are known and the length of at least one side is known then all the other sides must have a fixed value as well. So BD can be determined using the law of sines. (During the exam the law of sines isn't necessary to calculate as long as you know this rule)

If you want to check this and determine the values for yourself then you can use the law of sines.

Statement 2 says that x=36
Remember, a triangle can have infinite dimensions which would still keep the angles consistent. so 2 is insufficient.

Hence, A

Given,

angle BAD = x
angle BDC = 2x
angle BCD = 2x

From this we can figure out that angle ADB = 180 - angle BDC = 180 - 2x
From this angle ABD = 180 - (angle BAD + angle ADB)
= 180 - (x + 180 - 2x)
= x

From choice 1) AD = 6. Since we know if two angles in a triangle are equal then the sides opposite that angles are also equal.
Since angle BAD = angle ABD = x
length of side BD = length of side AD
Therefore BD = 6.

Since the angles opposite BD abd BC are each 2x(equal)
BC should be equal to BD.

Hence A is enough to solve this problem.