Forceps delivery is done in all except:
Option ‘a’
Mentoposterior: Before going on to mentoposterior, lets see mentoanterior.
Mentoanterior
​Dutta Obs. 7/e, p 390
In mentoanterior face presentation there is place for spontaneous vaginal delivery and liberal episiotomy is all that is required. In case of delay, forceps delivery is done.
In mentoposterior: 20 to 30% cases rotate anteriorly through 3/8 of circle and deliver as mento anterior, there fore trial of labour may be given in hope of anterior rotation of chin, followed by spontaneous/forceps delivery. In the rest 70-80%, incomplete anterior rotation/ non rotation occurs.
In these persistent mentoposterior: cesarean section is the only management. Therefore in mentoposterior per se forceps is not applied, only when it rotates anteriorly and becomes mentoanterior, forceps are applied.
Option ‘b’
Deep transverse arrest
Management options in case of deep transverse arrest are:
Dutta Obs. 7/e, p 372
Ventouse: Ideal for all cases
Cesarean section: If the pelvis is android or there is CPD, cesarean section should be done. In modern obstetrics, traumatic vaginal delivery causing intracranial hemorrhage is to be avoided at all costs and so there is increasing use of cesarean section for deep transverse arrest.
Other options are:

Manual rotation followed by outlet forceps application.
Forceps rotation and delivery using Keilland forceps.
Craniotomy if the baby is dead.

As far as options ‘c’ and ‘d’ are concerned: In after coming head of breech, and in heart disease forceps are routinely applied.
Mentoposterior
Deep transverse arrest
After coming head
Maternal heart disease