After their birth all four princes started growing together. When Raam was only 12 years old, Vishwaamitra Jee came to  Raaja Dashrath to take Him to save his Yagya from Maareech, Taadakaa and Subaahu like Raakshas. Dashrath loved Raam very much. He didn't want to send Him with Vishwaamitra Jee as He was very very young, but on Vashishth Jee's advise he got ready to send Raam and Lakshman along with Vishwaamitra Jee. He took them for 12 days only. Vishwaamitra Jee gave Him several weapons to help Him kill Raakshas before arriving at his Aashram. Raam used them to kill Taadakaa and Subaahu and hit Maareech. Then there was a Dhanush Yagya at Janak Puree, so Vishwaamitra Jee took them to Janak Puree also to show them that Yagya.

On the way to Mithilaa, they saw a dense forest where a huge rock was lying. Vishwaamitra Jee asked Raam to touch that rock with His foot. Raam asked the reason behind it and touched it with His foot. Immediately the rock was converted into a beautiful woman. She was Ahilyaa - Gautam Muni's wife. By the Shaap of Gautam Muni she was lying there for many years. She prayed Raam and went to her husband.

Then they arrived at Mithilaa Puree. In Mithilaa, Raajaa Janak welcomed them and asked Vishwaamitra Jee the introduction of the two boys who were with him. Vishwaamitra Jee told him that they were the sons of Ayodhyaa king Dashrath - Raam and Lakshman. 

When in the morning Raam went to royal gardens to pluck some flowers for Guru's Poojaa (worship), He saw Seetaa there who came there for Gauree Poojan with Her friends. Raam showed Seetaa to Lakshman and told Him that She was the girl for whom this Swayamvar was organized.

Vishwaamitra Jee took them to the Yagyashaalaa (place of the Yagya being done) and requested Janak Jee to show that Dhanush (bow) to Raam. There Janak Jee got that Dhanush carried by 5,000 men. Raam lifted it up and as He pulled the string, it broke in two. When it broke it made a great sound in whole Trilok.

My Note
Here Maanas has described the coming of Parashuraam after hearing the sound of breaking the Dhanush right in the Yagyashaalaa, Lakshman-Parashuraam dialog, and then Parashuraam's defeat by Raam very nicely, but Raamaayan brings him later - when Raajaa Dashrath was returning to Ayodhyaa and there is no Lakshman-Parashuraam dialog there. Even Parashuraam tlks very little with Raam also. In all it is a brief and presented as an unimportant incident. See below.

This was the condition of Seetaa's marriage that whoever will break this Dhanush, he will be able to marry Seetaa. So according to that their marriage was done but Janak Jee performed the formal ceremonies according to their family traditions. He  invited Raajaa Dashrath from Ayodhyaa and asked his permission if he accepted his another daughter Urmila for Lakshman and his brother's two daughters - Maandavee and Shrutkeerti for Bharat and Shatrughn respectively.

Raajaa readily accepted. All four brothers were married to four princesses. Janak gave a lots of things to Raajaa Dashrath. When he was going back to Ayodhyaa, they met Parashuraam Jee. He was very angry. He wanted to try whoever had broken the Dhanush. Raam said - "I tried to lift it up and it broke." Parashuraam Jee tried to give his own Dhanush to Him if He could pull its string, but it went itself. Parashuraam Jee was very surprised to see this and he went to Mahendra Parvat.

King came to Ayodhyaa with his four sons and four daughters-in-law. Palace echoed with people's laughter, music, and celebrations. They all stayed there in Ayodhyaa happily for about 12 years.