what are my chances when my family can pay only $6000/year

OP, talk to the schools on your current list. If you would like additional options, look at these pages. they list some of the schools that give the best financial aid to international students:

http://thecollegematchmaker.com/65-colleges-give-generous-aid-international-students/

https://lendedu.com/blog/international-students-financial-aid-study