The term ‘Sankat Mochan’ means the person who solves all the problems without backing off! Lord Hanuman perfectly fits the description of this term.
It doesn’t matter if it is hard or impossible to solve, he is someone who will somehow bring a solution to an issue using his Keen Intelligence. Lord Hanuman is quick-witted in nature. Nothing in the three realms is beyond his potential to accomplish. He can go anywhere at any time and can do anything at any time. No one in the three realms would dare to stop him. He is Unstoppable even by the strongest of the strongest forces.
When all the vanaras were reluctant to take a jump to Lanka, Hanuman was the only one who not only took a jump to Lanka but also came back safely without a scratch after burning the entire golden city of Lanka into ashes. He came back with a piece of info from his Mother Seetha Devi which was assigned to him as a task by Lord Rama. This Incident clearly shows his attention to detail and the way he respected and followed the orders and instructions given by Lord Rama and acted accordingly.
During the course of the war, Lord Hanuman protected his teammates from all sorts of danger. He always had their back, no matter what. Being Infinitely Strong, he was still humble, friendly, and never boasted about himself. His humility was off the charts!
When Indrajeet invoked Brahmastra on the troops of Lord Rama, the impact was very powerful and destructive. It took the lives of 670 million vanaras instantly killing them on the battlefield. Shree Lakshman passed out too. However, Lakshman Ji was just keeping the honor of the missile presided by Lord Brahma. During circumstances like these, everyone would lose hope and back off! However, Lord Hanuman was the first to come forward to aid his team in a hopeless situation like this one. He flew to the Himalayas from Lanka with a speed equal to the momentum of Garuda Ji or you could say with the speed of thoughts. He easily uprooted a huge mountain and carried it with one hand from the Himalayas to Lanka within a brief amount of time, that mountain consisted of a celestial herb named Sanjeevani. Once he brought the mountain to Lanka, he revived all the warriors who passed away from the impact of Brahmastra and brought everyone back to life including Lord Lakshman. In this way, he saved the lives of all the vanaras and Lakshman Ji using his wit and physical strength. It was so smart of him to bring the entire mountain instead of wasting the time trying to locate the celestial herb in the mountain.