It means praising a person's merits in public, but correcting and admonishing his shortcomings and faults in private.

Promote goodness: promote good deeds.

Specification: correct mistakes, correct mistakes.

Extended data:

Zeng Guofan was a controversial figure in the late Qing Dynasty. He has both the reputation of a famous minister of ZTE and the notoriety of "traitor". No matter who admires or despises him, his letters from home are highly praised. It can be seen that his letter from home is not only a collection of letters recording his daily life, but also a book with the wisdom of treating people and educating children.

The rise of Zeng Guofan had a far-reaching impact on the politics, military affairs, culture and economy of the Qing Dynasty. At Zeng Guofan's initiative, he built the first ship in China, founded the first ordnance school, printed and translated the first batch of western language books, and arranged the first batch of students studying in the United States. It can be said that Zeng Guofan was the pioneer of China's modernization.

References:

Baidu encyclopedia-promoting goodness

Baidu encyclopedia-turtle fruit

Baidu Encyclopedia-Zeng Guofan