If the line $\left(\frac{x}{2}+\frac{y}{3}-1\right)+\lambda \left(2x+y-1\right)=0$  is parallel to X–axis, then $\lambda$  is

$\frac{x}{2}+\frac{y}{3}-1+2\lambda x+\lambda y-\lambda =0$

$\left(\frac{1}{2}+2\lambda \right)x+\left(\frac{1}{3}+\lambda \right)y-1-\lambda =0$

If any line is parallel to $x-axis$  is  $x-$ coefficient is zero

$\frac{1}{2}+2\lambda =0$

$2\lambda =-\frac{1}{2}$

$\lambda =-\frac{1}{4}$