Making a hexagon from four sided face I am trying to model this:


The part that is giving me trouble is the small bolt shaped safety valve on the bottom section.

It's a hexagon so I could model it alone by using a six sided cylinder mesh.
But I have no idea how to implement this with my existing mesh, which is below:
In your case it really doesn't seem to be necessary to model this all joined together into one continuous mesh, but if you really want to try erasing two faces instead of just one, it will make topology a lot easier.

Erase two faces from the side of your conical surface, then use the Bridge Edgeloops operator to join the two resulting 6 edge loops.