From the information given,
arc AB is congruent to arc CD
chord AB = 6x - 2
chord CD = 3x + 13
If two arcs in a circle are congruent, then their corresponding chords are congruent. This means that
chord AB = chord CD
6x - 2 = 3x + 13
Collect like terms. We have
6x - 3x = 13 + 2
3x = 15
x = 15/3
x = 5