펴다 is flattening or straightening something that was folded, curled or bunched up — a T-shirt laid out before folding (봐요, 이렇게 펴고...), a hand opened flat (손을 꼭 이렇게 펴서?), butter spread thin (버터랑 함께 얇게 펴 발랐어요). -게 gives the manner and is nearly always 이렇게 here, with someone demonstrating. Its neighbour 펼치다 leans toward opening something out to show it; 펴다 leans toward getting it flat.