#### Answer

$(0, +\infty)$

#### Work Step by Step

First, solve each simple inequality to have:
Inequality 1:
$2x+4 \gt 0
\\2x \gt -4
\\x \gt -2$
Inequality 2:
$4x \gt 0
\\x \gt 0$
Thus, the given compound inequality is equivalent to $x \gt -2$ and $x \gt0$.
$x \gt -2$ includes all the numbers to the right of $-2$.
$x \gt 0$ includes all the numbers to the right of $0$.
The compound inequality involves the conjunction AND, which means that the solution will be the set that contains the numbers that are common to both sets.
The numbers that are common to both sets are the ones to the right of $0$.
Therefore, the solution is $(0, +\infty)$