How to solve∠1∠1 is a supplement of ∠2∠2 , ∠1∠1 is a complement of ∠3∠3, and m∠1=68∘m∠1=68∘. find m∠2−m∠3m∠2−m∠3?

You should note that complementary angles sum up to 90° while supplementary angles sum up to 180°. With that being said, the two equations we could formulate are:

∠1 + ∠2 = 180°
∠1 + ∠3 = 90°

Since ∠1=68°, we can solve for ∠2 and ∠3.
∠2 = 180 - 68 = 112° 
∠1 = 90 - 68 = 22°
The difference would be ∠2 - ∠1 = 112 - 22 = 90°