I'm skeptical solely based on the ridiculous number of double bonds that must be present in a molecule like that...
So, the number of moles of water gives the number of moles of hydrogen atoms in the organic compound. Similarly, the number of moles of carbon dioxide is the number of moles of carbon atoms in the original compound.
8.19 g of water has 8.19/18*2 moles of hydrogen atoms => 0.91 mol hydrogen, which is 0.91 g hydrogen (these are hydrogen atoms, not hydrogen molecules!). Why? 8.19/18 is the number of moles of water molecules and each water molecule has two hydrogens.
Number of moles of CO2 is then 20.2/44 mol = 0.459 moles of CO2 and hence carbon atoms. The mass of carbon atoms in the original compound is then 5.51 g. In total, we've accounted for 6.42 g of stuff in the organic compound. This leaves 8.20g - 6.42g = 1.78g of oxygen atoms, which is 1.78/16 = around 0.11 mol oxygen atoms.
Putting this altogether, we have 0.11 mol O, 0.91 mol H and 0.45 mol C. Ratio looks like 1 O to 4 C to 8 H to me i.e. C4H8O, which could be anything from a cyclobutanol (not very stable those things) to tetrahydrofuran (very stable solvent; five membered ring) or a ketone or even an aldehyde. None of these contain carbon-carbon double bonds.