What is the oxidation number of NH4OH?

NH4 itself is called ammonium ion with positive charge of 1+. hence the oxidation state will be + 1

OH itself is called hydroxide ion with negative charge of 1-. hence the oxidation state will be - 1

there's actually no such compound as stated in your chemical formula. although it's simply called ammonium hydroxide by looking at the chemical formula, in fact the compound should rightly be called as aqueous ammonia with chemical formula of NH3 (aq). this is because the ammonia molecule will ionise due to the presence of water molecule to be protonated, hence forming ammonium ion and hydroxide ion in the solution.