A clean way to attack this question is to first sort all four protecting-group families that could appear on an exam, match each reagent in the options to the family it removes, and then see which families match "MEM ether."
- $Pd/C$, $H_2$: this reagent pair is the classic deprotection for benzyl-type groups ($Bn$, $Cbz$) that have a benzylic C-O or C-N bond, through catalytic hydrogenolysis. A MEM ether has no benzylic bond and no double/triple bond, so this reagent simply does not react with it.
- $ZnBr_2$: this is a mild oxophilic Lewis acid. Its textbook use is exactly to remove MEM ethers, by binding the acetal oxygen and helping the $C-O$ bond to the substrate alcohol break, releasing the free $ROH$. This matches the transformation shown.
- PPTS, $^tBuOH$: PPTS is a weak acid catalyst (much milder than $TsOH$), commonly used in an alcohol solvent under heating to solvolyze acetal-based protecting groups such as $THP$ and $MEM$ ethers back to the free alcohol without disturbing acid sensitive parts of the rest of the molecule. This also matches.
- $^nBu_4NF$: this delivers a naked fluoride ion, whose only job in synthesis is to attack silicon and cleave silyl ethers ($TMS$, $TES$, $TBS$). There is no silicon anywhere in a MEM ether, so fluoride has nothing to react with here.
Matching reagent families to protecting group chemistry this way shows that only the Lewis acid ($ZnBr_2$) and the mild Bronsted acid in protic solvent (PPTS/$^tBuOH$) belong to the category of reagents that cleave acetal-type protecting groups like MEM.
Let's summarize:
- $Pd/C$, $H_2$ removes benzylic protecting groups, not acetals.
- $^nBu_4NF$ removes silyl protecting groups, not acetals.
- $ZnBr_2$ and PPTS/$^tBuOH$ both belong to the acid-catalyzed acetal cleavage family that removes MEM ethers.
The correct options are (B) and (C).