Answer: These are the right answers:
7. limpien
8. pongan
9. salgas
10. haga
11. que vayamos
12. que estudien
13. pasen
Explanation: Just to elaborate a little on the answer, it can be added that in this exercise they are asking you to complete the sentence with the right form of the verb in brackets. The mood that you must use is the subjunctive, which refers to information or actions that are more a possibility than a fact: "It is important that <em>you clean</em> the house," "I advise you <em>to not go out</em> with him," and so on.
Answer:
1) Yo neccesito que organizar mi cuarto los lunes.
2) Mi mama tiene que hacer la lavenderia.
3) Yo no quiero lavar los platos todos los dias.
4) El nessecita que sacar la basura.
5) Ellos no nessecitan que darle de comer al perro cuatro vezes al dia.
hope it helps