The basic problem with your example is that $result is wrapped in single-quotes. So the first solution is to unwrap it, eg:
$result = 'Hello';
echo '{
"result":"'.$result.'",
"count":3
}';
But this is still not "good enough", as it is always possible that $result could contain a " character itself, resulting in, for example, {"result":""","count":3}, which is still invalid json. The solution is to escape the $result before it is inserted into the json.
This is actually very straightforward, using the json_encode() function:
$result = 'Hello';
echo '{
"result":'.json_encode($result).',
"count":3
}';
or, even better, we can have PHP do the entirety of the json encoding itself, by passing in a whole array instead of just $result:
$result = 'Hello';
echo json_encode(array(
'result' => $result,
'count' => 3
));