Need help in creating MySQL trigger
This is very straightforward.

There is no == operator.

Please change

IF(New.LossTo == 'Vehicle') THEN


to

IF(New.LossTo = 'Vehicle') THEN


UPDATE 2018-02-26 11:04 EST

You need to change the delimiter before and after the trigger:

DELIMITER $$
DROP TRIGGER IF EXISTS TRG_CREATE_INT_SRV_ROW $$
CREATE TRIGGER TRG_CREATE_INT_SRV_ROW
 AFTER INSERT ON survey_details
 FOR EACH ROW
BEGIN
 IF(New.LossTo = 'Vehicle') THEN
    INSERT INTO survey_vehicle (RefNo) VALUES (New.RefNo);
 ELSE
    INSERT INTO survey_other (RefNo) VALUES (New.RefNo);
 END IF;
END $$
DELIMITER ;


Please see my old post Unique combination key MySQL for an example