宫以沫看在眼里十分嘚瑟的补充 宫以沫 is a name. I'm not sure how this should sound in English, nor how it should be translated. What I found didn't quite fit with the context it was being used in, so I'm confused...
Could you perhaps... give us the context? So we don't end up making the same translation as you? Anyway, 嘚瑟 typically refers to making a mountain out of a molehill in terms of being far more proud than what was actually accomplished, and 补充 just means added on, conversationally? Can't tell without context.
Oh, yeah, sorry! So, Gong Yi Mo has come up with a solution for Xi Zhou's yearly drought. She just explained how it would work, and now, she's about to say something else that is beneficial to her goals. (Something like that)
她说的清晰简单，在场的人闻言皆如醍醐灌顶，眼前一亮。 宫以沫看在眼里十分嘚瑟的补充，“此工程十分浩大，但是做成了却是一劳永逸的事，如此看来，十万兵马还是少了的，而镇西王常年戍边，已有威望，让他来调和督建，最是合适，父皇，我说的可对？” I feel like I can’t find the right English words to describe it. She observes/perceives/discovers their reaction and very smugly adds to what was previously said
My guess would be that she saw their reaction to her solution, became proud of herself, and was going to continue her explanation. Suggestion: "Seeing this, she proudly added..." with 'this' referring to their reaction