Ahh I used to be one too, then I became both after a while 😉 It’s inevitable in a small business
Anyway, this should do it provided that both fields are arrays!
<?php
$checkboxValues = get_field('field_name'); //Change field_name to your checkbox field
$morecheckboxValues = get_field('field_name_2'); //Change field_name to your checkbox field
$extraClasses = array_merge($checkboxValues, $morecheckboxValues);
?>
<?php post_class( $extraClasses ); //This goes in your <article> element (or whatever you use) ?>