selling price = list price - list price*0.1 <--this is the correct equation.
selling price = cost + cost*0.2 <-- he marks up his cost 20% to establish his selling price.
SP = $192.
192 = LP - 0.1LP = 0.9LP
LP = 192/0.9 = $213.33 <-- this is the list price the wholesaler should establish.
a 10% discount for this price is $21.33 off, for a sell price of $192.
what you have done is calculate a 10% markup of his selling price.