Bu = Butyl
Me = Methyl
The first one is two ketones reacting with base; K+ -OC(CH3)3 =KOtBu.
And, if you see aldehyde or ketones with base, you should think of aldol condensation where one of alpha proton is removed and attaches to the carbon carbonly group. Then if you see a HEAT, lose water(H2O), forming double bond between carbon carbonyl group and alpha carbon of attached molecule.
second problem is just epoxide reaction on basic solution, where you would attack less substituted carbon on epoxide.
Third question is just E2 reaction where Br is removed and foring cyclohexene. whenever you see a Br attached to the secondary carbon, and you see a strong base like NaOCH3, NaOH, NaOC2H6.
And the last one KO+Bu, I think this should be K+OBu, a strong base.
Please correct me if I am wrong