갖다 is the shortened form of 가지다 'have, hold', and it works two ways in these lines. With -고 it means possessing or carrying: 갖고 있다 'have it', 갖고 다니다 'carry it around', 갖고 오다 'bring it'. Directly before another verb it means 'take it and…': 갖다 쓰다 'take and use', 갖다 대다 'hold it up against', 갖다 주다 'bring it to someone'. -게 supplies the manner or the amount, and note that the amount reading covers time too: 10년 넘게 갖고 있었던 거야 'I'd had it for over ten years'.