The given statement is

" If $x$ is real number such that $x^3+4x=0$, then $x$ is 0."

Let $p :$ If $x$ is real number such that $x^3+4x=0.

and

$q:$ $x=0$.

To show that the above statement is true using contradiction method,

Let us assume that $p$ is true.

and $q$ is not true.

$i.e.,$ $x$ is a real number such that $x^3+4x=0$ and $x\neq 0$

$\Rightarrow\:\:x(x^2+4)=0$

$\Rightarrow\:$ either $x=0$ or $x^2+4=0$

But our assumption is $x\neq 0$ and

also $x^2+4$ cannot be $0$ since $x^2 \geq 0\:\: \forall x \in R$

$\therefore$ $x^3+4x$ cannot be equal to zero which is contradiction.

$\therefore$ $x$ should be equal to $0$.

$\therefore$ The given statement is true.