Students were given the task to fully simplify:

John's error: John incorrectly assumed that any number raised to the zero power equals 1, which is not true in this case.

Carol's error: Carol incorrectly calculated the exponent, she added 2 and -6 instead of subtracting.

To solve the expression correctly:
(2^2.2 - 6) - 3 x (2^0)
= (4.924 - 6) - 3 x 1
= (-1.076) - 3
= -4.076

Therefore, the correct answer is -4.076.