An ideal gas is held in a canister of volume V, at pressure P, and temperature T. Subsequently, the movement of a piston doubles the volume (to 2 V), while the temperature is also doubled (to 2 T), in absolute units (e. g. Kelvin). What is the new pressure

Using the ideal gas law we can determine this:

PV = nRT

n and R are constants but V and T are doubled:

that is the same as multiplying the entire equation by 2:

2 (PV) = 2 (nRT)

Therefore if we distribute we can get what is wanted:

P*2V = n*R*2T

Which then shows that pressure would stay constant if temperature and volume were to both double.