= Solution
Acid protonates one methoxy group of <2,2-Dimethoxypropane>. <methanol> departure gives the oxocarbenium species $\mathrm{Me_2C(OMe)^+}$, which is captured by one diol <oxygen>. After <proton> transfer, <protonation> and loss of the remaining methoxy group generate a second oxocarbenium center. Intramolecular attack by the other diol <oxygen> closes the five-membered ring; <deprotonation> regenerates acid. The net <transacetalization> exchanges two methoxy groups for the two diol oxygens, releasing two <methanol> molecules.
\b[The two starred <carbon> centers retain their original configurations, and the two <carbon> side chains on the <acetonide> are trans.] No C–O bond at either original <stereocenter> is broken; reaction takes place at the reagent-derived CMe$_2$ acetal <carbon>. The apparent change in wedge/dash presentation comes from redrawing the backbone into the five-membered ring, not inversion at a starred center. In the planar pentagon used in the diagram, draw the alkynyl-bearing side chain behind and the $\mathrm{CH_2OPMB}$ side chain in front. The unstarred methyl-bearing center also retains its <configuration>. The acetal <carbon> itself is not stereogenic because its two methyl substituents are identical.
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