Are these two sentences right using "I stopped?"

gerund object - I stopped to fix the flat tire.

infinitival object - I stopped fixing the flat tire.

No.

Please see my last explanation.

So my sentences should be:

I stopped to fix the flat tire. (infinitival)
I stopped fixing the flat tire. (gerund)

Is this correct?

Yes. :-) Now you've got it!

Yes, both sentences are grammatically correct and use the phrase "I stopped" correctly. However, they have slightly different meanings.

In the first sentence, "I stopped to fix the flat tire," the phrase "to fix the flat tire" functions as a gerund object. This means that the action of stopping is done in order to perform the action of fixing the flat tire. The focus is on the subsequent action in this sentence.

In the second sentence, "I stopped fixing the flat tire," the phrase "fixing the flat tire" functions as an infinitival object. This means that the action of stopping is done while in the middle of fixing the flat tire. The focus is on the action that has been interrupted or ceased in this sentence.

To identify the type of object in a sentence, you can look for the words that follow the verb "stopped." If the words are in the format of "to + verb" (e.g. "to fix"), it is a gerund object. If the words are in the format of "-ing" (e.g. "fixing"), it is an infinitival object.