So technically you don't need laravel for this. You could hold all the time slots in an object in JS and do something like the following (not complete code, more like pseudo code)
const slots = {
8to9_available: 'true',
9to10_available: 'true',
//etc...
}
Then we you click on the enroll button, you have a JS function that just checks against that array....
function checkAvailability(slot) //slot should be formatted 8to9available
{
if(slots[slot]) //objects can be accessed as arrays, and this is checking if it's value is true
{
// make an ajax request to register
}else{
// show error message
}
}
This would keep this logic on the front end, perhaps in aVue or a React component and eliminate a DB hit.