That's a good strategy above, however the event you want to listen for is simply 'resize', on the window object (some older browsers can do it on any dom element, but better to be consistent and current with the standard).
So something like:
window.addEventListener('resize',function(){
if(window.innerWidth >= 768){
document.body.style['overflow-x'] = 'hidden';
}
else{
document.body.style['overflow-x'] = 'auto';
}
});
You can trade 'auto' for 'scroll' if you want the scrollbar to always show when less than 768.
Similarly, you can switch out 'overflow' instead of 'overflow-x' if you want to affect both scrollbars.
Keep in mind that the event tends to fire for every width and height change as the window is resized, in case you have other logic that might have an issue with firing many times (thousands or more) as it is resized.
This also works on maximize/restore, as they trigger the resize event as well.
Here's MDN's doc on the resize event if needed:
https://developer.mozilla.org/en-US/docs/Web/Events/resize
This is vanilla javascript, so it should work whether you're using a lib like jquery or not.