You're really close - you're actually just missing one word in your code.

Side note - you can use the "{...} code" button in this editor to make your code easier to read.

$(document).ready(function() {
    $('.Submit').hide();

    $('.toolInventory .checkMe').click(function () {
        var anyChecked = false;
        $('.toolInventory .checkMe input').each(function() {
            if ($(this).is(':checked') && $(this).val() === 'Check_Out') {
                anyChecked = true;
                return false; // Exit early if any checkbox is slected
            }
        });

        if (anyChecked) {
            $('.Submit').show();
        } else {
            $('.Submit').hide();
        }
    });
});

The only change I made to your code was on line 6 - I added the word "input". 

If you examine the structure of the fields within your form, you'll see that the fields are actually a div element which contains a lot of other components such as labels, error containers, text above and below the field, etc.  The class name (in this case checkMe) is applied to that top-level div element.  We need to find and focus specifically on the input element(s) within the checkMe div, not on the div itself.

Hope this helps, and have a good day!