First, you need to think about limiting reactors : we see that 3 moles of F2 will react with 1 mole of Cl2.
Here, F2 is the limiting reactor because all 150 cm3 of F2 will be used, whereas only 50 cm3 (1/3 of 150) of Cl2 will be used. There will be an excess of 50 cm3 of Cl2.
At the end, 3 moles of Cl2 will give us 2 moles of ClF3. So 150cm3 → 100 cm3 of ClF3.
Then you just add up the excess reactant (50cm3) with the product (100cm3) and you have the final gaseous volume : 150 cm3.