Draw the diagram to show the geometry.
m∠AEC = 4x, mAC = 120, and mDB = 2x.
There is an Intersecting Chord fact that says that the angle at the intersection, m∠AEC, is half the sum of the angles of the circumference (measured at the circle centre), ie (mAC + mDB)/2 = 4x.
(mAC + mDB)/2 = 4x.
(120 + 2x)/2 = 4x
60 + x = 4x
3x = 60
There's a handy summary of Geometry Facts here. This one is Section R (d).
Hope this helps.