From the table, poly(ethylene) has a solubility parameter of 7.9 cal cm.  Good solvents are likely to be diethyl ether and hexane. (However, PE only dissolves at temperatures well above 100 °C.)  Poly(styrene) has a solubility parameter of 9.1 cal cm, and thus ethyl acetate is likely to be a good solvent.  Nylon 6,6 has a solubility parameter of 13.7 cal cm, and ethanol is likely to be the best solvent of those tabulated.  However, the latter is polar, and thus we should be very cautions about using just the Hildebrand solubility parameter to make predictions.