Whenever we are talking about gases, the first thing that always comes to my mind is the ideal gas law, PV = nRT. In this problem, we can look at the information we are given to see if that is a usable equations. We have volume, temperature, and pressure given in the problem and R is our gas law constant so we can solve for the moles of gas, n.
The challenge with this problem is that everything is in different units than what we need. For the ideal gas law, we want pressure in atm, volume in L, and temperature in Kelvin.
Let's convert each of them to the right units
752 mmHg (1 atm / 760 mmHg) = 0.989 atm
1200.0 cm^3 (1 mL / 1 cm^3) (1 L / 1000 mL) = 1.2000 L
32 degC + 273 = 305 K
Now, we can plug everything in and solve for n.
(0.989 atm)(1.2000 L) = n (0.08206 L atm/ mol K)(305 K)
n = 0.0474 mol He