Components connected across V-Out usually has a very high effective resistance compared to R1 and R2. The voltage divider formula is only an approximation of what actually happens.
In this case, however, the component connected across V-Out is a simple resistor, and it has the same resistance as R2. Hence, treat it as a simple resistor circuit.
In most resistor circuits Vout doesn't automatically have the same resistance as R2...
They specified the resistance to be 4.4kohms
"a load of resisoance 4.4k ohms is conected across the output terminals"
But if you take it as just the 4.4k ohms then the solutions are wrong?
See attached
The solution (Vout = 3) is incorrect, it should be Vout = 4.5