Triple click on the geometry to select it all. Then right click on it and choose Intersect Faces>With Selection. After that erase the unneeded edges. Also remember to correct any reversed faces. There should be no exposed blue back faces.
I would also suggest that you move the object to the origin and keep it there. You can wind up with strange graphical issues if you don’t.
By the way, is this something you intend to 3D print? If so, I would suggest modeling it as if millimeters are meters. That will help you avoid issues with tiny faces leaving holes that prevent your object from being manifold.
I redrew your model that way. For the crossing tube I rotated the cylinder so that therewere edges parallel to the axes which prevents that tube from meeting at the vertices on the vertical holes. It’s another way to prevent potential holes from forming.