Here's why:
* Direct object: The direct object is the thing that receives the action of the verb. In this case, the direct object is "a salad".
* Indirect object: The indirect object is the person or thing that benefits from the action of the verb. "Her" is the person who benefits from the salad being made.
You can test this by rearranging the sentence:
"He made a salad for her with many fresh tomatoes."
This structure clearly shows that "her" is the recipient of the salad.