It requires a lot of practice and trial and error. I usually encounter problems when solving tasks like this one.
Here you had a liquid oxide. The most famous liquid oxide is water, so you assume that it is water, you calculate its quantity and compare, e.g. with the gaseous oxide. If they got formed in 1:1 ratio, then the gaseous oxide has a molar mass of 44g/mol which corresponds to few gasses, but a good guess would be carbon dioxide (because when acidic or basic carbonate salts decompose, they can form solid oxide, water and carbon dioxide). You do the same for the solid oxide. Assume 1:1 ratio, and you will get a very big molar mass that doesn't correspond to any simple oxide I can think of. Then try the 2:1 ratio, and you will end with a molar mass of 223g/mol. Now you assume that there is one oxygen atom in the oxide, so the other element that composites the oxide has a molar mass of 207g/mol (Pb). Now you need to pack these oxides into one compound. As you see, many assumptions have to be made.