!n is a red herring. For any value of x other than 0, !n will be false; it will be true when x == 0.

m is 0 for even numbers, 1 for odd numbers. When you compare a number with a boolean, the boolean is converted to a number. So m <= false is equivalent to m <= 0. This will be true when m is 0.

So you can get rid of n and just use this:

function isEven(x){
   var m = x % 2;
   return m <= false
}

[0, 1, 2, 3, 4, 5, 6, 7, 8].forEach(x => console.log(x, isEven(x)));

The reason why it works with !n is because in the only case where !n is true, x == 0 and m == 0. 0 <= true is true, so the function returns the correct result then as well.

First

var n = x / 2

n will be falsey if x is 0, and truthy otherwise.

If the argument is even and not 0:

• m will be 0
• n will be a truthy number (because anything divided by 2 is another non-zero number - except 0)
• !n will be false (because that's the boolean inverse of 0, a falsey value)
• the return statement is 0 <= false; false gets converted into a number when compared with <=, and 0 <= 0 is true

If the argument is odd and positive:

• m will be 1
• n will be truthy (because any odd number divided by 2 is another non-zero number, and a non-zero number is truthy)
• !n will be false (because that's the boolean inverse of a truthy value)
• the return statement is 1 <= false; false gets converted into a number when compared with <=, and 1 <= 0 is false

If the argument is even and 0:

• m will be 0
• n will be 0
• !n will be true (boolean inverse of 0)
• the return statement is 0 <= true; true gets converted into a number when compared with <=, and 0 <= 1 is true

But the code doesn't work when the argument is odd and negative, because a negative odd number % 2 gives -1, not 1.

• m will be -1
• n will be truthy (because any odd number divided by 2 is another non-zero number, and a non-zero number is truthy)
• !n will be false (because that's the boolean inverse of a truthy value)
• the return statement is -1 <= false; false gets converted into a number when compared with <=, and -1 <= 0 is true - when it should be false