The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

For second overtone (3rd harmonic) in open organ pipe,
$\frac{3\mathrm{\lambda }}{2} = {\mathrm{l}}_0 \Rightarrow \mathrm{\lambda } = \frac{2{\mathrm{l}}_0}{3}$
For first overtone (3'd harmonic) in closed organ pipe,
$\frac{3\mathrm{\lambda }}{4} = {\mathrm{l}}_{\mathrm{C}} \Rightarrow \mathrm{\lambda } = \frac{4{\mathrm{l}}_{\mathrm{c}}}{3} = \frac{4\mathrm{L}}{3}$

$\mathrm{So}, \frac{2{\mathrm{l}}_0}{3} = \frac{4\mathrm{L}}{3} \Rightarrow {\mathrm{l}}_0 = 2\mathrm{L}$