Coordinate Geometry: JEE Main 2022 Mathematics question

A common tangent $\mathrm{T}$ to the curves $\mathrm{C}_{1}: \frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ and $C_{2}: \frac{x^{2}}{42}-\frac{y^{2}}{143}=1$ does not pass through the fourth quadrant. If $\mathrm{T}$ touches $\mathrm{C}_{1}$ at $\left(x_{1}, y_{1}\right)$ and $\mathrm{C}_{2}$ at $\left(x_{2}, y_{2}\right)$, then $\left|2 x_{1}+x_{2}\right|$ is equal to ______________.