Determine a resistor's value in a circuit with an N-type MOS-FET transistor
For \$V_D=8\rm{V}\$, the quiescent current (through the MOSFET) is \$I_D=\frac{16\rm{V}-8\rm{V}}{1.2\rm{k\Omega}}=6.67\rm{mA}\$. Knowing that the transistor must be in saturation, you use the equation for saturation drain current:
$$I_D=\frac{k}{2}(V_{GS}-V_{TH})^2$$
Of course, transconductance parameter \$k\$ and threshold voltage \$V_{TH}\$ must be known. From this equation, you can solve for \$V_{GS}\$, which here is equal to \$V_G\$, and, in combination with the voltage divider equation \$V_G=\frac{R_2}{R_1+R_2}V_{DD}\$, you can solve for \$R_2\$.