Okay... two CH3's connected to oxygen sounds right for the peak at 3.5. Since they are equivalent you could bet that they are both -OCH3's connected to the same carbon. If they were connected to different carbons their magnetic environment would probably be different slightly and so they would appear as two singlets.
Now if you have two -OCH3 groups on one carbon, that carbon might have the CH (triplet) around 4.7. If that were the case it would have to be next to a CH2 to give the triplet. The CH2 at around 2.6 is a doublet (from coupling to the CH) so that fits as well.
Now all you have left is the final 3H singlet which is probably a CH3 group not next to any protons to couple with. Since the molecular formula is C6H12O3 you also have to account for another carbon and oxygen - a ketone to separate the CH3 and the CH2 should do the trick. Put it all together and you get ... (see attached)
These things are just like solving puzzles. You need to know roughly where various types of protons appear (chemical shifts) and then piece together the info from the coupling patterns, numbers of protons, and the molecular formula.