좋아한다고 말하게 하고 싶다 => I want to make him/her say that he/she loves me. ('좋아한다고 말하게' lacks both the subject and object, so this is just a most probable meaning.) '-게' is a verb ending indicating causing an action or bringing about some effect from a person or thing. It's similar to -도록 in meaning but is less formal and more widely used. In this example, 말하게 하다 (or 말하게 만들다) means making someone say something. - 아이가 울지 않게 얼렀다 = I tried to please the baby to keep him from crying. - 학교에 늦지 않게 일찍 일어났다 = I got up early not to be late for school. - 입은 옷과 어울리게 검은 모자를 썼다 = I wore a black hat to make it go with my clothing.