Eerst moet je de grootste datum voor elke cheque vinden
SELECT `check`, MAX(`datetime`)
FROM YourTable
WHERE `service` = 2
GROUP BY `check`
Doe dan weer mee om de rest van de gegevens te krijgen.
SELECT Y.*
FROM YourTable Y
JOIN ( SELECT `check`, MAX(`datetime`) as m_date
FROM YourTable
WHERE `service` = 2
GROUP BY check) as `filter`
ON Y.`service` = `filter`.service
AND Y.`datetime` = `fiter`.m_date
WHERE Y.`service` = 2