In "The Legend of Zhen Huan", Yunli (i.e., King Guojun) finally confirmed that Hongyi was his son through a series of clues and speculations. Although this process is not explicitly shown in the play, it can be inferred from the details and logic of the plot.
First of all, the emotional clues between Yunli and Zhen Huan are one of the important clues of the entire plot. In the play, Yunli and Zhen Huan have a deep relationship, but for various reasons, they did not end up together. However, Yunli has always been obsessed with Zhen Huan, and her feelings for her have always been the same.
Secondly, Hongyi's appearance came after Yunli and Zhen Huan had been separated for a long time. When Hong-yu appeared at the court, Yun-ri quickly noticed what made him special. He observed that Hongyong's eyes, mannerisms, and personality were very similar to Zhen Huan's, which made him start to suspect that Hongyong might be his son.
In addition, Yunli also obtained some clues through other channels. For example, he may have learned from other palace maids, eunuchs, or other people in the court about the emotional entanglement between Zhen Huan and the emperor, as well as the fact that the son born to Zhen Huan was the emperor. These clues also helped him to be more convinced of his suspicions.
Finally, Yunli asked her about Hongyi's life experience through private contact with Zhen Huan. Although Zhen Huan did not directly tell Yunli Hongyu that it was his son, from her words and expressions, Yunli could already confirm that his guess was correct.
To sum up, Yunri finally confirmed that Hongyu was his son through various methods such as observation, speculation, and inquiry. Although this process is not explicitly shown in the play, it can be inferred from the details and logic of the plot.