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1. The IR peak at 1740 indicates carbonyl compound. This is good since there's so many oxygens in the compound. Since there's six oxygens, one might think of three ester groups. That would take care of 6 C.
The triplet at 1.3 integrated to 9H means that there's probably three CH3 groups each adjacent to a CH2 group. The quartet at 4.2 integrated to 6H matches the three groups of CH2 we just mentioned. Therefore, we've got three ethyl groups so far. Since the quartet matching the three methylene groups are shifted so far (4.2), I'd suggest that the oxygens of the ester groups are adjacent to the CH2 groups.
Therefore, we've got so far three of these:
That accounts ...
The solution provides detailed explanations for explaining IR peaks, and a diagram for the mechanism of an esterification reaction.