[tex]f_{yy}[/tex] is the second partial derivative with respect to [tex]y[/tex]:
[tex]f(x,y)=3x^2+2x^4y^2+6y^3[/tex]
[tex]\implies f_y(x,y)=4x^4y+18y^2[/tex]
[tex]\implies f_{yy}(x,y)=4x^4+36y[/tex]
Then at the point [tex](x,y)=(1,1)[/tex], we have
[tex]f_{yy}(1,1)=40[/tex]
