Since we need 4/3 liters of water to water 2/5 of the plants in the house, then we need
[tex]\frac{4}{3}\div\frac{2}{5}\text{.}[/tex]of water to water all the plants.
Recall that:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}\text{.}[/tex]Therefore:
[tex]\frac{\frac{4}{3}}{\frac{2}{5}}=\frac{4\times5}{3\times2}\text{.}[/tex]Simplifying the above result, we get:
[tex]\frac{20}{6}=\frac{10}{3}\text{.}[/tex]Answer:
[tex]\frac{10}{3}\text{ liters.}[/tex]