You can find the oxidation number of a certain element in a compound if you add up their oxidation numbers to the net charge. This is just a simple algebraic equation. Let x be the oxidation number of Cr. Since the compound is neutral, the net charge is 0. Thus,
oxidation number for Li: +1
Oxidation number of O: -2
0 = 2(+1) + x + 4(-2)
Solving for x,
x = +6
Thus, the oxidation number of Cr is +6.
