Here are some hints! There are lots of possible structures, but to get an even number of hydrogens in Compound B, we need to multiply its empirical formula by 2. Doing that to the formula of Compound A also, you get the following still simple formulas to work from:
Compound A: C6H12O2
Compound B: C6H10O2
1) What is the degree of unsaturation of these compounds? That is helpful information.
2) Can you think of an oxidation reaction that lowers the number of hydrogens by two? You have probably seen oxidations of alcohols and aldehydes; what happens to the formulas after the oxidation?
>> provide all possible structures of Compound A and of Compound B <<
In principle, there are an infinite number of possibilities, depending on what factor you multiply the empirical formulas by, for starters! Does the problem give you any additional information, such as a molecular weight?
Steve