Transconductance of a nmos transistor
Well \$g_m = \frac{\Delta I_D }{ \Delta V_{GS}} \approx \frac{3.7A - 2A}{6V - 4V} \approx \frac{1.7A}{2V} \approx 0.85\; S \$ 

For \$V_{GS2} = 6V, I_{D2} = 3.7A\$ and \$V_{GS1}=4V , I_{D1} = 2A\$

But this way was already shown. 

But from the plot, we can also find \$V_{TH}\$ using this equation: 

$$V_{TH} = \frac {V_{GS1} \sqrt{I_{D2}} -V_{GS2} \sqrt{I_{D1}}}{\sqrt{I_{D2}} - \sqrt{I_{D1}}} $$   

And \$K_P\$ factor

$$K_P=\left ( \frac{\sqrt{2I_{D1}}-\sqrt{2I_{D2}}}{V_{GS1} - V_{GS2}} \right )^2$$ 

But in your case, these equations do not give any sensible results. 
So there is something wrong with your plot.