How to calculate this resistor MOSFET circuit?
The schematic shows an Enhancement mode Nch.  The circuit exceeds  the typical threshold for Vgs(th) = 0.5~4V putting the drain into the "linear" mode where linear and saturated modes are opposite to BJT's.  So BJT's Vce drops &lt;1V when saturated while FET's drop in voltage to a low RdsOn when in "linear mode".

Since you calculated correctly Rload to be 240, much higher than typical RdsOn &lt;10, your conclusion is also correct. 

Thus 240 Ohms is the sum of Rd and RdsOn


  There is no way the drain can be 5V. 


It will be reduced by the R ratio of RdsOn/(RdsON+Rd) * V+ (near 0V)

Here a Nch MOSFET is shown with some arbitrary Drain current for Vgs above Vth on the x axis. and thus is a linear voltage controlled resistor until that resistance curve saturates or flattens out. 

Rds will pull down the 240 Ohms by the some unknown amount based on the rated RdsOn @Vgs=6V  If RdsOn was 10 Ohms Vd= 0.5V

Again this x axis is the Vgs-Vth difference.



A saturated BJT has Vce&lt;1V
A saturated MOSFET has Vds > saturation threshold of a parabolic curve where Id will not increase with Vds.  Thus in Saturation mode with large Vds, Id=constant current controlled by Vgs.  


In the "linear" region a MOSFET will act as a Voltage control switch of some RdsOn with low Vds to the left of the parabola.

The X axis scale could be in xx mV for millohm type MOSFETs.
another graph here shows in log-log Vds vs Id for a Pch