[LazyPup]

you cannot snake a tub through the drain opening. You must remove the overflow cover and snake through the overflow pipe. If you have a lever type stopper on the overflow cover you remove the screws for the cover then pull out and upwards at the same time and the stopper will come out.

I am attaching an illustration that will show you how the pipes are laid out. From the illustration you can see then when you insert a snake into the overflow it will go straight down to the trap.