Answer
$12 \text{ hours}$
Work Step by Step
Let $x$ be the time it takes for Tom to type the mailing labels alone.
In terms of $1$ unit/part, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{6}+\dfrac{1}{x}=\dfrac{1}{4}
.\end{array}
Multiplying both sides by the $LCD=
12x
,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
12x\left(\dfrac{1}{6}+\dfrac{1}{x}\right)=\left(\dfrac{1}{4}\right)12x
\\\\
2x(1)+12(1)=3x(1)
\\\\
2x+12=3x
\\\\
2x-3x=-12
\\\\
-x=-12
\\\\
x=12
.\end{array}
Hence, it will take $
12 \text{ hours}
$ for Tom to type the mailing labels alone.