First you give 4 volunteers the card with the numbers 1 to 15. They choose one between them and keep it secret.
Next you give them the four special cards with numbers and letters on, one each, in the order as below.
These are special in that the numbers on each one matter. Secretly think of them as card 8, card 4, card 2 and card 1. These are the numbers in their top left corner of the card.
Stand the volunteers in a line and give out the cards in that order, so the person on the right facing you has card 1 and the person on the left has card 8.
Now you get those with their chosen number on their card to close their eyes. You add up the card numbers of the people closing their eyes and that is their secret number.
So if the people holding card 1 and card 8 have closed their eyes and the other two volunteers are staring at their card, eyes open, then add 1 and 8 and announce they are thinking of number 9.
If instead the people holding card 2, card 4 and card 8 have their eyes closed then the secret number is 2 + 4 + 8 so 14.
It is that simple. You don’t need to be able to read minds. Instead, you set up a secret way, using the cards, for their chosen number to leak out. In computing, a way information can secretly leak out of a system like that is called a ‘covert channel’.