There are a few ways to get from Mannlichen to Horner Pub in Lauterbrunnen. You can walk the most direct way, or the longer less direct way, or use a train for much of the way. If you look at either of the AllTrails maps linked below, you see a loop hike. They are similar, but AllTrails 2 is slightly longer. The short way is to walk the northern part of either loop hike to Lauterbrunnen. The long way is to walk to Kleine Scheidegg and walk the southern part of either loop to Lauterbrunnen. Going the long way, i.e. heading south from Berghaus Mannlichen at the start, you go to Kleine Scheidegg. There, you have the option of taking the train down. Another, even shorter option, is to take the cable car from Berghaus Männlichen down to Wengen, and then walk down from there. The trail between Mannlichen and Kleine Scheidegg is called the, "Panorama Trail", and is supposed to have good views.