= Solution
\b[A is the kinetic, less-hindered-side <silyl enol ether>.] Its double bond lies away from the methyl substituent. Forming B requires removal of a <proton> from the more hindered $\alpha$ position adjacent to the methyl-bearing carbon.
The base strengths alone do not determine the ratios. <trimethylsilyl triflate> is strongly electrophilic: oxygen silylation activates the <ketone> towards deprotonation, and irreversible trapping of the resulting <silyl enol ether> can make the product ratio reflect competing deprotonation rates. A weak <amine> therefore need not first produce a substantial equilibrium concentration of the free <ketone> <enolate>.
DBU is the strongest and comparatively accessible base, and distinguishes the two sites least strongly, giving the smallest A:B ratio. Triethylamine gives greater preference for the less-hindered site. The more sterically hindered diisopropylethylamine discriminates most strongly and gives the largest proportion of A. Its slightly higher conjugate-acid $pK_a$ than that of triethylamine does not reverse this trend, because \b[steric accessibility and the coupled silylation/deprotonation mechanism matter alongside basicity]. The data do not establish a simple thermodynamic <enolate> distribution.
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