Damaged Exterior Drain Pipe Fitting
This isn't going to be something easy to fix for most
do-it-yourselfers. The arrow in the picture above is pointing to a crack
that runs all the way around the cast iron waste pipe fitting.
If something like this is left unrepaired for a long enough time, you could find your self dealing with foundation problems. As the water leaks out of the waste pipe regularly, it could start to wash away the soil that's underneath the structural building foundation.
Home Repair Tip: Cut above the cast-iron fitting and below the cast-iron fitting at least 4 inches. This damaged exterior drain pipe fitting hooks up to the bathroom sink drain. Disassemble the drain from the inside and you should be able to remove the damaged fitting safely.
You can use cast-iron or plastic, the choice will be up to you. If you're comfortable working with one material more than the other, then by all means use that material.
You will need to purchase a new plumbing fitting and this type of plumbing waste pipe is called a san tee. Make sure that you install the san tee correctly. You do not want to install it upside down.