The Chain Rule & Implicit Differentiation · Superchallenge problem

A smooth function $f(x,y)$ satisfies the wave equation $f_{xx} = f_{yy}$ everywhere. Along the line $y = 2x$ it is known that $f(x, 2x) = x$ and $f_x(x, 2x) = x^2$ for all $x$. Find $f_{xx}(3, 6)$.