Loop Through Categories in Custom Field

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The way you’re appending a foreach loop to a variable is not possible.

Try this:

$form_fields["custom4"]["html"] = "<select name="attachments[{$post->ID}][custom4]" id='attachments[{$post->ID}][custom4]'>";

foreach ($categories as $category) {
     $form_fields["custom4"]["html"] .= '<option value="$category">' . $category . '</option>';
}

$form_fields["custom4"]["html"] .= "</select>";