This question related to the concepts of Young's Double Slit Experiment
Here, we will use only one concept:
Path Difference for nth bright fringe = n*Lambda
Here, let us name:
Known wavelength = Lambda1 = 590 nm
Unknown wavelength = Lambda2
We are given that the Central Maxima of both lights coincide. This means that there is no initial path difference between the two lights.
Now, third bright fringe of known wavelength light coincides with the fourth bright fringe of the unknown wavelength light.
So, we can write:
3Lambda1 = 4Lambda2
3*590 = 4Lambda2
Lambda2 = 442.5nm