अपनी मत पर चलना apnī mat par chalnā

अपना apnā (hindi)

Reflexive possessive pronoun and adjective : my, mine, myself, your, yours, yourself, etc.

चलना chalnā (hindi)

Continue.

मत mat (sanskrit)

Opinion, view. Doctrine (which contains the author's opinions).

पर par (hindi)

पर denotes :

• Location or position on or upon or at something.
• Point of time at which an action takes place.
• Sequence of actions of happenings.
• Cause or reason.
• Objects of (compound) Verbs signifying mercy, faith, confidence, anger etc.
  (A Basic Grammar of Modern Hindi)