The interest is on number ##4##,
In my working,
##f(x,y,z) = x+y^2+2z## and ##g(x,y,z) = 4x^2+9y^2-36z^2 = 36##
##f_x = 1, f_y=2y## and ##f_z = 2## and also ## g_x = 8λx, g_y = 18λy## and ##g_z = -72λz##
using ##\nabla f (x,y,z) = λ\nabla f (x,y,z)##
i shall have,
##1 = 8λx ##
##2y =...