Hey there! 
C₃H₆O(l) + O₂(g) => CO₂(g) + H₂O(g) 
First thing I want to do is balance the equation. Balance C: 
C₃H₆O(l) + O₂(g) => 3CO₂(g) + H₂O(g)
Balance H: 
C₃H₆O(l) + O₂(g) => 3CO₂(g) + 3H₂O(g)
Balance O: 
C₃H₆O(l) + 4O₂(g) => 3CO₂(g) + 3H₂O(g) 
Now we can properly solve the problem. 
a.)
Density of acetone is 0.800 g/mL, we need to form 67.2 L of CO₂ at STP. 
For every one mole of acetone reacted, 3 moles of CO₂ is produced. 
Let's convert 67.2 L to moles: At STP, one mole of a gas takes up 22.4 liters. 
67.2 ÷ 22.4 = 3 moles 
So turns out we want to produce 3 moles of CO₂, which means we need one mole of acetone. 
The molar mass of acetone is 58.08 g/mol. The density of acetone is 0.800 g/mL. We need the volume of one mole. 
58.08 ÷ 0.800 = 72.6 
72.6 mL of acetone is needed. 
b.) 
For every one molecule of acetone reacted, 3 molecules of water is produced. 
We are combusting 3.011 x 10²² molecules of acetone. 
3.011 x 10²² x 3 = 9.033 x 10²² 
Find the number of moles: 
(9.033 x 10²²) ÷ (6.022 x 10²³) = 0.15 moles
The molar mass of water is 18.015 g/mol.
0.15 x 18.015 = 2.7 grams 
2.7 grams of water vapor is formed. 
Hope this helps!