$Y = max(0,X)$
so value generated by $Y$ would depend on value of $X$
$case\ 1 :$ when $X<0$ then $Y = max(0, -ve)=0$
$case\ 2 :$ when $X =0$ then $Y =max(0,0)=0$
$case\ 3 :$ When $X >0$ then $Y = max(0,X)=X$.
So what would be the sequence of values generated for $Y$ ?
$....... \underbrace{0,0,0,0,0,0,0}_{\text{when X is negative}}\ 0\ \underbrace{1,2,3,4,5,6,7}_{\text{when X is positive}} ......$
This is because $X$ is a Gaussian random variable $\implies$ its curve would be same as that of normal distribution.
We know curve of normal distribution is always bell shaped and is split into $2$ equal halves by the mean value.
and in question it is given that $mean = 0$ so half the values of $X$ would be $-ve$ and half of them would be $+ve$
For every $-ve$ value of $X$ , $Y=0$ and for every $+ve$ value of $X$, $Y=X$
Now what is median ?
The middle value of among a sequence is called median , like median of $0,2,2, 3,9$ is $2$ because $2$ is at the middle.
Similarly for this sequence
$\underbrace{0,0,0,0,0,0,0}_{\text{when X is negative}}\ 0\ \underbrace{1,2,3,4,5,6,7}_{\text{when X is positive}}$
the median would be $0$
hence median of $Y$ = middle value among the sequence $=0$