Convert the months to a numerical value. Then order your array numerically using sort()
You can use this question: convert month from name to number
@Matthew’s answer seems to work well:
$date = date_parse('July');;
echo $date["month"];
Working solution
$months = array("April", "August", "February");
usort($months, "compare_months");
var_dump($months);
function compare_months($a, $b) {
$monthA = date_parse($a);
$monthB = date_parse($b);
return $monthA["month"] - $monthB["month"];
}