What is the chemical formula for Y and O?

And of course, oxygen, a Group 16 element, commonly forms #O^(2-)# ions....

When yttrium metal, and oxygen gas combine, the simple oxide is of course neutral with respect to charge. And so we cross-multiply in the usual way: #2xxY^(3+) + 3xxO^(2-)rarrY_2O_3#...aka #"yttria"#...

(This reminds me of an old joke of a colleague of mine who worked in our lab. Anyway, we worked with a lot of rare earths, and when we ran low, he told us to grab a spade, go over to Ytterby in Sweden, and dig up some ytterbium, yttrium, terbium, and erbium, and some scandium and holmium and thulium.)

Yttrium is a metal and oxygen a non-metal - because non-metals tend to gain and metals tend to lose electrons, metals typically react with non-metals by transferring electrons between them and forming ionic compounds ('salts').

Yttrium has the electronic configuration Kr 5s2 4d1. This means that it tends to react by losing 3 electrons and forming a 3+ ion. Oxygen forms 2- ions by gaining 2 electrons. Therefore, 2 yttrium atoms transfer 6 electrons to 3 oxygen atoms, making two yttrium 3+ ions and three oxide (2-) ions and thus the formula of yttrium oxide is #Y_2O_3#.