The first thing we do in a problem like this is let arc AB equal X. X is the magic letter, anything you need to find name it x. We also know that all arcs in a circle must add up to 360, so arc ALB is equal to 360 - x.
There's this theorem saying that when two tangents intersect from a point outside a triangle, the measure of the angle formed by the intersection of the tangents (angle P) is equal to the half the difference of the arcs.
This basically means:
angle P = 1/2(360 - x) - x.
plug in the value of angle P
84 = 1/2(360 - x - x)
168=360 - 2x
2x = 192
x = 96
arc AB=96
