Final answer:
The question seems to contain a typo in the velocity function and cannot be solved without the correct expression. The distance traveled would be found by integrating the velocity's absolute value over the time interval, but this isn't possible with the given information.
Step-by-step explanation:
To find the total distance traveled by the referee from time t = 2 minutes to t = 6 minutes when the velocity is given by v(t) = 4(1 - 6)cos(21 + 5), we need to integrate the absolute value of the velocity function over the given time period, as distance is the integral of speed(not velocity, as velocity can be negative whereas speed cannot).
However, the given velocity function seems to have a typographical error since '1 - 6' and '21 + 5' don't align with standard mathematical expressions. Assuming that this is a typo, and possibly meaning v(t) = 4(1 - t)cos(2t + 5), we would proceed to integrate.
Unfortunately, due to the possible typos present in the velocity function, we are unable to accurately find the total distance traveled without the correct function.