Answer: 1960
Explanation: The question says:
Since which year Amalia's ballet started to perform in the Palacio de Bellas Artes?
This question is about the ballet of Amalia Hernandez.
In January of the year 1960, the ballet presented for the first time in the Palacio de Bellas Artes under the name of "Ballet Folklórico de Bellas Artes."