Jotta Everyone,

It is generally known that the events in the Itihaasas have symbolic interpetations that go beyond their meaning as literal events.
There is a significant possibility that Sri Rama's exile of 14 years from Ayodhya falls in this category.
The Srimad Bhagavata Mahapurana states that there are 7 heavenly realms and 7 hellish realms: 7 + 7 = 14.
Sri Rama could have spent his exile traveling through these realms, spending one year in each.