You should show your whole code. What you’ve posted above won’t output at all. Additionally there is no need to assign a variable as you have a value already…
your field values are set in ACF this way for a radio button:
white : White
light-grey : Light Grey
dark-grey : Dark Grey
(notice the space around the colon)
Now for your code:
$bg = get_field('background', $post->ID);
if( $bg ) {
$background = $bg['value'];
} else {
$background ='';
}
echo '<div class="mybackground '.$background.'">hi there</div>';
then your css:
.white {
background-color:white;
}
.dark-grey {
background-color:grey;
}
.light-grey {
background-color:#f0f0f0;
}
You will need to customize a bit for what you’re actually doing but this should work.
If you have format value set to just return value then change this line:
$background = $bg['value'];
to this:
$background = $bg;