Answer
$$r(t)=\lt1+3t, t,4-2t\gt$$
(Other answers are possible.)
Work Step by Step
Since the line passes through $(1,0,4)$ and $(4,1,2)$, then the direction vector is given by $$(4,1,2)-(1,0,4)=\lt3,1,-2\gt$$
and the equation of the line is given by
$$r(t)=\lt1+3t,0+t,4-2t\gt=\lt1+3t, t,4-2t\gt$$
