Когда я пишу связку for надо ли после неё написать the ?

mom, dad,  i quit  and come back  later,  because  i was going  to celebrate  the birthday of  a friend  in a cafe.  please  do not worry, i  will come  exactly  at 11 p.m.

1).his machines work better than their machines.

2). my holiday expenses are larger than her holiday.

3). the parking space in my region is more expensive than in his region.