Since YZ is the perpendicular bisector of AB, we know that:
AN = NB = 3x (since YZ bisects AB)
AB = 24 (given)
We can also see from the diagram that the total length of AB is equal to the sum of AN and NB:
AB = AN + NB
Substituting in the values we know, we get:
24 = 3x + 3x
Combining like terms, we get:
24 = 6x
Dividing both sides by 6, we get:
x = 4
Therefore, the value of x is 4.