Final answer:
The easiest method for an attacker to access a password with unlimited attempts in ActiveSync is through a brute force or dictionary attack, as it methodically tries all possible passwords.
Step-by-step explanation:
The easiest method an attacker can use to gain access to a password if ActiveSync allows an unlimited number of password attempts is by using a brute force or dictionary attack. This approach systematically checks all possible passwords until the correct one is found. Since ActiveSync does not limit the number of attempts, this makes it particularly vulnerable to such attacks. While keylogger installation or password guessing could also potentially be used, a brute force or dictionary attack is the most straightforward method given the lack of attempt limitations.