I miscarrige december 06 2013 but i haven't had a cycle yet i took a at home pregnancy test it's positive as on january 24 2014 how is this possible ?

Possibilities:: It is possible that you conceived again - though that is less likely the further along that you were; the other possibility - is that you may have some pregnancy hormones left over in you blood from the pregnancy. By 6 weeks later 95%of patients with have cleared the hormones from their systems. A small, but significant thing to check is that there isn't any 'left-over' pregnancy tissue in uterus.