#### Answer

$h=\dfrac{12}{5}$

#### Work Step by Step

Multiplying both sides by the $LCD=
24
$ and then using the properties of equality, the value of the variable that satisfies the given equation, $
\dfrac{h}{4}+\dfrac{h}{6}=1
,$ is
\begin{array}{l}\require{cancel}
6(h)+4(h)=24(1)
\\\\
6h+4h=24
\\\\
10h=24
\\\\
h=\dfrac{24}{10}
\\\\
h=\dfrac{\cancel{2}\cdot12}{\cancel{2}\cdot5}
\\\\
h=\dfrac{12}{5}
.\end{array}