@AjayMishra hi :-)

Sorry, I thought you aren't here.

is the coefficient of friction independent of direction?

In this question, since the box is not slipping along the incline, I assume that $ \mu_{current} = \tan 20, \implies P = W \sin 20 $, but I am getting $26.8 N$ which is wrong.

@AjayMishra In real life the friction often depends on the direction, but in questions like this you can assume the friction is the same in all directions unless the question specifically tells you otherwise.

What is wrong in my assumptions?

There is a force down the slope. The total force is the vector sum of the force P and the force down the slope.

The block slips when the total force exceeds $\mu m g \cos20$.

But why downward component would affect the magnitude of horizontal[or along the perpendicular to this inclination of the incline]

The block is not constrained to move in the horizontal direction. What will happen is that as you increase P the block will start to slip at some angle given by the relative magnitudes of the two forces.

Ahh, I got it, I thought the direction of slipping would be in the direction of force.

Yes :-)