Answer
The numbers are $63$ and $21$
Work Step by Step
Let the first number is $x$ and second number is $y$
Given,
One number is three times a second number,
$x=3y$ Equation $(1)$
Twice the sum of the numbers is $168$
$2(x+y)= 168$
$x+y=84$ Equation $(2)$
From Equation $(1)$ and Equation $(2)$
$x+y=84$
$3y+y=84$
$4y=84$
$y=21$
Substituting $y$ value in Equation $(1)$, we get,
$x=3y$
$x=3(21)$
$x=63$
The numbers are $63$ and $21$