Step 1: Reaction type.
The transformation shown is an acid-catalyzed elimination (\(E1cb/E2\)-like, via BF\(_3\)·OEt\(_2\)) of the alcohol to form an alkene. For stereospecific elimination, the \(\beta\)-hydrogen and the leaving group (OH after activation) must be in an anti-periplanar orientation.
Step 2: Analyze stereochemistry of G.
The substrate G has two adjacent stereocenters: one bearing the OH group and a methyl, the other with bulky substituents. To generate the observed alkene product, only those stereoisomers where the \(\beta\)-H is anti-periplanar to the OH can undergo elimination.
Step 3: Evaluate the options.
(A): Conformation allows the required anti-periplanar alignment → productive.
(B): Has syn-periplanar OH–H alignment → not productive.
(C): Mirror stereoisomer of (A) with correct anti arrangement → productive.
(D): Syn relationship again → not productive.
Step 4: Conclusion.
Therefore, only stereoisomers (A) and (C) give the depicted alkene product.