The ketone shown is treated with LDA in THF at $-78^{\circ }$C and then with one equivalent of methyl iodide. Which structure shown is the major product?

The ketone shown is butan-2-one. LDA at low temperature gives the kinetic enolate at the less substituted CH${}_3$ carbon, and this enolate reacts with $\mathrm{CH}{}_3\mathrm{I}$ at carbon. Methylation of the CH${}_3$ group gives pentan-3-one; methylation of the CH${}_2$ side (thermodynamic enolate) would give 3-methylbutan-2-one.