If the sum of the numbers $5x9$, $327$ and $2y8$ is $1114$, then the largest value $y$ can take is:

Expressing the numbers according to their place values:
$$5x9=500+10x+9$$
$$327=300+20+7$$
$$2y8=200+10y+8$$
Summing them up:
$$(500+10x+9)+327+(200+10y+8)=1114$$
$$1024+10x+10y=1114$$
$$10(x+y)=1114-1024$$
$$10(x+y)=90⟹x+y=9$$
For $y$ to be the largest single digit value, $x$ must be at its minimum possible value. Since $5x9$ is a 3-digit number, the minimum value for the digit $x$ is 0.
$$0+y=9⟹y=9$$