The root that author decided to take but could not is given as:

Kathmandu → Patna → Varanasi → Allahabad → Agra → Delhi

Other possible routes are :

Kathmandu → Birgunj → Raxual Junction → Nizamuddin Railway Station (Delhi)

Kathmandu → Kasauli (Nepal) → Sonauli → Gorakhpur → Delhi

Kathmandu → Birgunj → Raxual Junction → Chennai Central Railway Station.

Consult a geography book to find other routes.