The professor suggested the problem referred to be solved at

The professor （主语）suggested （谓语）.
宾语从句
the problem（主语） referred to（=which had been referred to是定语）（should 省略了） be solved at once
去掉修饰语
.（suggested) the problem (should) be solved(被动语态）
suugest "建议“ 接句子时用虚拟语气（should)+动词原形
全句意为 “教授建议所提到的那个问题应该马上予以解决”
请及时采纳,不懂继续问( 天天在线 ）