What does the HTML markup look like for the checkboxes? Assuming you're using names like "ckbx", "ckbx", etc. then $_REQUEST['ckbx'] will be an array; this:
won't exist for two reasons:
Variable interpolation doesn't occur within single quote delimited strings, thus you're telling PHP to look for an array index of "ckbx," followed by a left square bracket, followed by a dollar sign, followed by... etc.
$_REQUEST['ckbx'] itself is the array; when you want to access a specific index in that array, the square brackets go on the end (not inside the key of the outer array, $_REQUEST).
Second, if checkboxes aren't checked, then they won't be included in the external data at all (since the user's browser won't send anything for those elements). Thus, you can use [man]isset/man to check if the given index in the array exists; if it does, the checkbox was checked, and if it doesn't, then it wasn't checked.