Question

what is the oxidation number of each atom in Cu(OH)2

Answer 1

The options are
Cu = +1, O = -2, H = +1
Cu = +2, O = -1, H = +1
Cu = +1, O = -2, H= -1
Cu = +2, O = -2, H = -1

Answer 2

The hydroxide ion on its own has a charge of -1. You have 2 of them here, so Cu must have a charge (and therefore an oxidation number) of +2 to cancel out the negative charge.

Looking at the hydroxide ion alone, the sum of the oxidation numbers must equal the charge on the entire ion, -1. Unless we're talking about the peroxide ion or oxygen gas, the O atom has an oxidation number of -2. This means H must have an oxidation number of +1, in order for the net charge on the ion to be -1.

It doesn't look like this answer is in any of your options though...