참다 is holding something in — an urge, laughter, pain, an irritation. In six of these eight lines the manner word is 어떻게 'how' (once spelled the dialect way, 우뜩케), used as a rhetorical 'who could possibly resist?': 이 비주얼을 어떻게 참냐고 'how are you supposed to resist something that looks like this?', 어떻게 참고 계세요? 'how do you have that kind of self-control?'. It also means enduring rather than reacting: 참는 게 미덕인 줄 알고 'thinking that holding it in was a virtue'.