2007 Chevy cobalt

Looks like the engine mount but more information would help. Where is this located in the engine compartment? I see a radiator hose, multi grove pulley and what looks like the motor mount below the hose.

Here’s a better picture rite behind exhaust

Middle of the car back of the engine compartment to the right of the exhaust in that one

Looks like the rear trans mount. I am assuming you are referring to the round thing. https://www.gmpartscenter.net/auto-parts/2007/chevrolet/cobalt/lt-trim/2-2l-l4-gas-engine/engine-cat/engine-and-trans-mounting-scat