Problem about finding distance with magnitude given A star in Pleiades cluster has apparent magnitude of +12 ($m_{star} = +12$) determine it's distance from the sun? (We know the Sun properties such apparent and absolute magnitudes, distance from earth, luminosity, brightness (energy flux) and others but nothing is given about the other star expect that apparent magnitude).

My problem is that we don't have luminosity of the star. We can say:

$m_{sun} - m_{star} = -2.5 * \log_{10}{\frac{b_{sun}} {b_{star}}} \Rightarrow 10^{(-26.8 - 12)/(-2.5)} \approx 3.31131 * 10^{15} = \frac{b_{sun}} {b_{star}} \approx \frac{1370 Wm^-2}{L_{star} / (4  \pi  d^2)} $

As we can see, we don't have luminosity of the star. Can this question be solved with this information?
Short answer: no, you can't solve the question if all you know is its apparent magnitude. It could be a faint star that's nearby, or a very luminous star that's far away. (The Sun's parameters are irrelevant.)

(I'm ignoring the bit about it being "a star in the Pleiades", which implies that it's a physical member of the Pleiades cluster, in which you already know its distance: it's the same as the distance of the Pleiades cluster. Maybe you just meant "it's in the same part of the sky".)