Answer
The percentage of gas ejected is $9.5\%$
Work Step by Step
At the start, the system of the astronaut, the propulsion unit and the gas inside is at rest, so there is no total momentum, or $\sum\vec{p_0}=0$
During the space walk, the gas (with mass $m$) is ejected and has the velocity $\vec{v_f}=+32m/s$. The astronaut and the propulsion unit (mass $M=165kg$) recoils with $\vec{V_f}=-0.39m/s$
The principle of conservation of linear momentum states that $$m\vec{v_f}+M\vec{V_f}=\sum\vec{p}_0=0$$ $$m_{ejected}=\frac{-M\vec{V_f}}{\vec{v_f}}=2kg$$
The total mass of gas in a completely filled propulsion unit is $m_{gas}=m_{gas\_left}+m_{ejected}=(165kg-146kg)+2kg=21kg$
Therefore, the percentage of gas ejected is $\frac{2}{21}\times100\%=9.5\%$
