Answer
$13\;\rm cm$
Work Step by Step
Let $L_1$ be the length of the open-open pipe and $L_2$ be the length of the open-closed pipe.
We know that the fundamental frequency of an open-open pipe is given by
$$(f_m)_{\rm open-open} = \frac{mv}{2L}$$
where $v$ is the speed of the sound wave.
And we know that the frequency of an open-closed pipe is given by:
$$(f_m)_{\rm open-closed} = \frac{mv}{4L}$$
And we are given that
$$(f_3)_{\rm open-open} = (f_1)_{\rm open-closed} $$
So,
$$\frac{ 3 \color{red}{\bf\not} v}{2L_1} = \frac{ \color{red}{\bf\not} v}{4L_2}$$
Thus,
$$L_2=\frac{2}{12}L_1=\frac{2}{12}\cdot(78)$$
$$L_2=\color{red}{\bf 13}\;\rm cm$$
