#### Answer

$3$ gallon-containers

#### Work Step by Step

A rectangular room with length$\times$width$\times$height dimensions of $14\times18\times8$ has two walls with dimensions $14\times8$ and two walls with dimensions $18\times8.$ Using $A=lw,$ the total area of these walls is
\begin{array}{l}\require{cancel}
A_{total}=2A_1+2A_2
\\
A_{total}=2(14)(8)+2(18)(8)
\\
A_{total}=224+288
\\
A_{total}=512
.\end{array}
Since $2$ coatings will be applied, then a total of $2(512)$ or $1024$ square feet will be painted. With each gallon of latex paint able to cover $400$ square feet, then a total of $3$ gallon-containers is needed.