Step 1: Understanding the Concept
Williamson synthesis uses an alkoxide and a primary alkyl halide in an \(S_N2\) reaction.
Step 2: Limitation
A tertiary alkyl halide gives elimination to an alkene instead of substitution.
Step 3: Check the options
Options A, B and C can all be made using a primary halide such as ethyl halide with a suitable alkoxide or phenoxide. Option D, di-tert-butyl ether, would need a tertiary halide on one side, so it cannot be prepared.
Final Answer:
Di-tert-butyl ether cannot be prepared by Williamson synthesis.
\[ \boxed{\text{(D) }(\text{CH}_{3})_{3}\text{C-O-C(CH}_{3})_{3}} \]