"I don't vacate in 4 weeks then father-in-law can proceed with his execution case as per law".
According to the aforementioned statement, if you will not vacate the property in 4 weeks then the Father-in-law may proceed for the execution proceedings of the decision made under Order XII Rule 6. In a view, the Court has decided the RFA in favour of your Father in Law and has give you four weeks time to vacate, Therefore, ultimately, you have to vacate the property, if you will not vacate it in 4 weeks, you have to vacate when the execution proceedings will be initiated. To simply it for you, execution proceeding is to bring into force the decision of the Court. So, if the Court has decided for your vacation then in execution proceedings, you will be made to vacate the property.
Now, coming to the second part. If you vacate the property yourself within 4 weeks then your husband has to pay one year advance rent to you. If you dont vacate then he is not liable to pay anything.
As I have not seen the complete order of the Court. I will also request you to confirm it from your counsel.
Thank you.