Answer
$$ (1,5,8)$$
Work Step by Step
The parametric equations of the line are given by
$$ x=1, \quad y=1+2t, \quad z=4t.$$
Now, substituting in the equation of the plane
$$ x+y+z=14\Longrightarrow 1+1+2t+4t=14\\
\Longrightarrow 6t=12\Longrightarrow t=2.
$$
So the point of intersection is given by $$(1,1+2(2),4(2)=(1,5,8)$$
