Is Nepalese passport eligible for 24 Hrs TWOV to go outside of the Airport?

Keshari, it is important to use correct terminology because there is no any kind of visa involved here, but a temporary entry permit is the detail that allows you to exit the airport. In any case, both of your flights are eligible for 24 hour visa free transit and you do not need any kind of visa. In reality, we have two situations with your itineraries. During your first layover, you will have just one stop in China. This is fine. The first thing you will do upon your landing in Chengdu you will approach 24/240 hour visa free transit counter where you will apply for a temporary entry permit by presenting your flight tickets and your hotel booking. You have to understand that the granting of the permit is based on discretionary decision of the Chinese authorities, but since your layover is very long, your chances to be granted a permit are practically certain. During your second leg, you will do the same thing, but in this case you will be granted a permit definitely for certain because you simply have to catch a flight from Chengdu to Beijing. In order to do that, you will obtain a permit and then head to the immigration in order to perform a change to a domestic flight to Beijing. In any case, you should carefully count your hours spent in China, especially during your second leg because the entire transit time is counted from the scheduled arrival in Chengdu until your scheduled departure from Beijing. You have written the time, but I am not 100% certain if you have written the time of your final departure from Beijing. In any case, you will be fine and I really hope that you will be issued a permit during your first layover. During the second one, it goes automatically. Have a nice journeys.