Redmine Admin wrote:
$eventId = "2";
$unitId = "2";
$clientId = "2";
$startDate = "2017-08-05";
$startTime = "13:00:00";
$endDate = "2017-08-06";
$endTime = "21:00:00";
$clientTimeOffset = "-3600";
$additional = array("name"=>"test");
$count = "";
$batchId = "";
$recurringData = "";
$services = $client->book($eventId, $unitId, $clientId, $startDate, $startTime, $endDate, $endTime, $clientTimeOffset, $additional, $count, $batchId, $recurringData);
here is PHP example for book method using Admin API