Correct spelling, explanation: caring is an adjective created from the verb care. Care ends with a silent e, so to create an adjective we have to drop the letter e and then add the suffix -ing. This rule shows us that spelling careing is not correct, because e was not removed. The correct spelling is only caring.

Definition of caring:
adjective: feeling or showing kindness, compassion, and concern to others;
My mother was a very caring person, she was always there for people when they needed emotional support.
I would like to be more caring, but people just annoy me.

Incorrect spelling, explanation: careing is the incorrect spelling of the adjective caring. Caring is created from the verb care, which ends with a silent e. To create an adjective from care, we have to remove e and add the suffix -ing. Therefore, version careing is not correct and the good version is caring.

Incorrect spelling