Answer
$\approx 10\;\rm g$
Work Step by Step
We know, for an ideal gas, that
$$PV=nRT$$
where $n=m/M_{\rm Ne}$ whereas $M_{\rm Ne}$ is the atomic mass of the neon.
Hence,
$$PV=\dfrac{m}{M_{\rm Ne}}RT$$
Hence,
$$P=\left(\dfrac{mR}{M_{\rm Ne}V} \right)T$$
The term between parenthesis is the slope of the $P {\rm -versus-} T$ function.
$${\rm Slope}=\dfrac{mR}{M_{\rm Ne}V} $$
Solving for $m$;
$$m=\dfrac{M_{\rm Ne}V\;{\rm Slope}} { R}$$
Plugging the known;
$$\boxed{m=\dfrac{(20.2)(2\times 10^{-3})\;{\rm Slope}} { (8.31)}}$$
So we need to draw the best-fit line of $P$ versus $T$ and then find the slope. We have to convert the given temperature data to Kelvin and the given gauge pressure to absolute pressure (by adding 1 atm to the gauge pressure) in Si units of Pascal.
\begin{array}{|c|c| }
\hline
T{\;(\rm K})& P{\;(\rm Pa}) \\
\hline
373 & 7.62\times 10^5 \\
\hline
423 & 8.92\times 10^5 \\
\hline
473 & 9.96\times 10^5 \\
\hline
523 &1.073 \times 10^6 \\
\hline
\end{array}
Now we need to plug these dots into a $P$-$T$ graph and then draw the best-fit line that connects them and then find the slope of this line. You can use any software calculator.
Plugging the slope from the figure below into the boxed formula above,
$$ m=\dfrac{(20.2)(2\times 10^{-3}) (2074)} { (8.31)} $$
$$m=\color{red}{\bf10.08}\;\rm g$$