My mother: "I like cooking." My mother said (that) she likes cooking. My mother said (that) she liked cooking

In your examples, the differences in the reported speech concern the verb tense used, which can convey different meanings or contexts.

1. Direct Speech: "I like cooking."

   • This is a present simple statement, indicating that your mother enjoys cooking at the present time.

2. Reported Speech: "My mother said (that) she likes cooking."

   • This retains the present tense ("likes"), suggesting that your mother continues to enjoy cooking at the time she spoke, or that her enjoyment is still relevant.

3. Reported Speech: "My mother said (that) she liked cooking."

   • This uses the past tense ("liked"), implying that her enjoyment of cooking was true in the past but does not confirm its current relevance. It can suggest that her feelings about cooking might have changed or that the statement refers to a past situation.

In summary:

• Use "likes" if you're reporting her statement while indicating it still holds true.
• Use "liked" if you're referring to a past enjoyment that may not be relevant now.