Answer
$\dfrac{12}{5} \text{ days}$
Work Step by Step
Let $x$ be the time it takes to finish the job when both work together.
In terms of $1$ part/unit, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{4}+\dfrac{1}{6}=\dfrac{1}{x}
.\end{array}
Using the $LCD=12x$ and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
12x\left(\dfrac{1}{4}+\dfrac{1}{6}\right)=\left(\dfrac{1}{x}\right)12x
\\\\
3x(1)+2x(1)=12(1)
\\\\
3x+2x=12
\\\\
5x=12
\\\\
x=\dfrac{12}{5}
.\end{array}
Hence, the time it takes to finish the job when both work together, $x,$ is $
\dfrac{12}{5} \text{ days}
.$
