Answer:The values of x and y that make the quadrilateral is a parallelogram are x = 12 and y = 21Step-by-step explanation:In the parallelogram, every two opposite sides are equal in lengthsIn the given figureIf DEFG is a parallelogram, then DE = GF and DG = EF∵ DE = GF∵ DE = 6x - 12 and GF = 2x + 36→ Equate them∴ 6x - 12 = 2x + 36→ Subtract 2x from both sides∵ 6x - 2x - 12 = 2x - 2x + 36∴ 4x - 12 = 36→ Add 12 to both sides∵ 4x - 12 + 12 = 36 + 12∴ 4x = 48→ Divide both sides by 4∴ x = 12∵ DG = EF∵ DG = 6y - 42 and EF = 4y→ Equate them∴ 6y - 42 = 4y→ Add 42 to both sides∵ 6y - 42 + 42 = 4y + 42∴ 6y = 4y + 42→ Subtract 4y from both sides∵ 6y - 4y = 4y - 4y + 42∴ 2y = 42→ Divide both sides by 2∴ y = 21∴ The values of x and y that make the quadrilateral is a parallelogram are x = 12 and y = 21