calculation

Since when it is cooled down to the room temperature, the product has been condensed to liquid water.
According to the given, no. of moles of water produced = 0.00083 moles which is equivalent to 0.015 g of water, i.e. 0.015 cm3.
Hence this is a negligible volume compared to that of those oxygen remained and therefore the volume remained is 10cm3.

30 is definitely not correct, as water is liquid form, not gaseous form.
The volume of liquid can be neglected.

Therefore, 20 cm3 of H2 will react with 10 cm3 of O2 to form water,
as the volume is neglected, we just consider the amount of gas remained.
Total volume of gas = 20+20 cm3 = 40cm3
Volume used during reaction = 20cm3+10cm3 = 30cm3
Therefore, volume left = 40-30 cm3 = 10cm3

You come up with the answer 30 as you are not neglected the presence of water, you are consider that they are steam! Therefore you find out the answer is 30.