Balance the reaction:
a Ag₂O + b O₂ → c AgO
Count the atoms on either side:
• Ag : 2a = c
• O : a + 2b = c
Suppose a = 1. Then immediately c = 2, and it follows that b = 1/2, so that the balanced reaction is
1 Ag₂O + 1/2 O₂ → 2 AgO
or, with integer coefficients,
2 Ag₂O + 1 O₂ → 4 AgO
This tells you that 4 mol AgO are produced for every 2 mol Ag₂O and 1 mol O₂.
Since 0.450/2 = 0.225 < 0.300, we end up consuming all of the starting Ag₂O, and produce 4/2 × 0.450 = 0.900 mol AgO.