:D
(http://www.math.toronto.edu/courses/apm346h1/20159/Forum/P2.6.2a.svg)
(http://www.math.toronto.edu/courses/apm346h1/20159/Forum/P2.6.2b.svg)
because plug x = 0 in U|_{t = 0} = Ï•(x), we will have
U|_{t = 0, x = 0 } = Ï•(0)
(1)
and plug x = 0, t = 0 in u(x,t)=4/3 Ï•(12x+t), we will have
U(0,0) = 4/3 Ï•(0)
(2)
conclude (1) and (2), we will have the answer by Fei Fan Wu