I’ll assume that you have Japanese Knotweed which is pretty common around here.  It spreads by underground shoots so dig out as much as possible getting every little bit of root you can see.  Then, cover the area with three or four layers of cardboard and cover the cardboard with some mulch like cedar mulch.  Leave it that way for a year.  Watch for any shoots that emerge and spray them with Round-up or a mixture of vinegar, Epsom salt and dishwashing soap.  Remember,…roundup or the vinegar solution will kill ANY AND ALL PLANTS so don’t get any on any plants you don’t want to kill.  You’ll probably see it popping up for years so this will be a long process…tough stuff to eradicate completely.