Answer
$7.705\;\rm \mu m$
Work Step by Step
As we see in the figure below, the second ray (ray 2) reflects with π-phase change.
And since we have 24 dark bands two of them are at the two ends of the upper glass piece.
The right edge has a dark band at which $m=0$, so the left edge has a dark band at $m=23$ since the total dark bands are 24.
The author here asks about the thickness of the foil, which is actually the thickness of the air film at the left edge between the two flat glass pieces.
Now we have a destructive interference at the edge where $m=34$ and we have two reflected rays with one phase change, so the thickness is given by
$$t=\dfrac{1}{2}m\lambda=\dfrac{1}{2}\cdot23\cdot 670$$
$$t=\bf7705\;\rm nm=\color{red}{\bf 7.705}\;\rm \mu m$$
