As shown in the picture, English. I don't quite understand whether there is a preposition after the verb. Thank you!

When laugh is used as a verb, you should use the preposition at instead of laugh sb. If you want to make fun of someone or laugh at …, you should say laugh at someone.

Chopsticks are used for eating, so tools are usually connected with chopsticks, for example, eating with chopsticks. They are already in front of the sentence, equivalent to kitchen knives. You can't say chopsticks are for eating, can you?