Direction of motion climbing up stairs for work problem

[Jewish_Vulcan]

The work does not have a direction so it does not make sense to say "there is no work in the horizontal direction".
It may be part of your initial confusion too, as well as the ambiguous formulation of the problem in OP.
"mgh" is not the "work done for a person climbing up a set of stairs" but is the (absolute value of) the work done by the force of gravity on that person. As gravity is always vertical, only the vertical displacement count for the work of this force.
There are other forces acting on the person and the work of these forces can have any values, depending on the specific problem. It is not necessary for the work of these other forces to be zero or have any specific value.

However, if the initial and final kinetic energies are the same (maybe zero) then the work of the net force will be zero (the work-energy theorem). Because gravity is doing -mgh, the work of all the other forces will add up to +mgh.

whatever... that response did not even help at all.

Why? Did they specify that it started from rest? If nothing is stated about the initial vs. final velocity you should naturally assume they are equal, but not necessarily zero.

I do not "assume facts", I am a very literal person.If they are more clear on the parameters of the problem I would have understood why there is a net force of 0 in the horizontal direction. That is like saying assuming that the velocity initial is 0 without them stating it!

 

[A.T.]

I do not "assume facts"

Standard textbook problems often expect you to make some obvious default assumptions. Otherwise, even a simple problem would look like some legal paper with pages of caveats. If unsure, assume the simplest case and state in the solution what you assumed. For extra points provide answers for different assumptions.