What is the error? NH4OH (aq) + KOH (aq) --> KOH (aq) + NH4OH (aq)
I don't see it, so can someone help.

Explanation:

The issue here is that none chemical reaction is happening.

The two compounds mixed are ionic bases: both of them dissociate in water producing OH⁻ ions:

Then, when you write the total ionic equation you have:

NH₄⁺(aq) + OH⁻(aq) +  K⁺(aq) + OH⁻(aq) →

                                                   NH₄⁺(aq) + OH⁻(aq) +  K⁺(aq) + OH⁻(aq)

Look at the species on the reactant side and the product side: the same ions are found on both sides.

That means that all of them are spectator ions: they are just dissolved, and remain in water (aqueous solution) without reacting. None new different compound is formed.

The net ionic equation would not have any species because the spectator ions get canceled.