The compound shown is warmed with a trace of dilute sodium hydroxide, and water is lost. Which structure is the major product?

The compound is 4-hydroxy-4-methylpentan-2-one, a beta-hydroxy ketone. Hydroxide removes the acidic alpha-hydrogen on C-3, and the enolate expels hydroxide from C-4 (E1cB). This gives the conjugated enone 4-methylpent-3-en-2-one (mesityl oxide), which is more stable than the non-conjugated isomer. Acetone would arise from the reverse aldol reaction.