This is a very simple INSERT .. SELECT query.
Just
The id is not included in the column list as it has the AUTO_INCREMENT property and will get values automatically. You only need to replace 'aaa' with the menucardhash value that you want to duplicate from and and 'qqq' with the new value:
INSERT INTO menuship3 (headhash, menucardhash, menucathash, producthash) SELECT headhash, 'qqq', menucathash, producthash FROM menuship3 WHERE menucardhash = 'aaa' ;