6.He (know)..a little english,so he wishes he ( can?speak).. it well

=> knows/ could

7. It's 8 am. he (work)... at the office

=> is working

8. You should(learn) how( keep)... the enviroment unpolluted

=>learn/ to keep

9. That is one of the city churches the ( destroy)...by bombing during the war

=>was destroyed

10.It is necessary (avoid)...(go)...out at rush hours

=>to avoid/ going 

  6. knows

      could speak

  7. is working

  8. learn

      to keep

  9. was destroyed

10. to avoid      (It is Necessary + to + [Verb in simple form] )

      going   (avoid + V_ing)