You didn't learn the 夏 reading with the kanji, so we'll have to come up with a mnemonic to remember the reading of summer solstice, especially the first half. Just think about how cute little geckos (げ) start to come out into the open during the summer solstice. It's too cold for them to be out in the open before that, so if you look outside at the right time, you'll see geckos popping out of the ground all over the place!
My dad asked me if I knew what to call the eleventh day after the summer solstice, so I said triumphantly "hageshou," which literally means "baldness-symptom". He laughed and told me the correct answer was "hangeshou."