During the second part of the installation process ( the part where it ask for your password); Adobe is not accepting my password and therefore, I cannot complete installation. How do I overcome this problem.
The Flash Player installer shouldn't be asking for your Adobe login. If you're asked for a password it would be the one for your computer system, to give permission to do the installation.
This is the OS, not Flash Player prompting for the password, as such, it's whatever you use (with admin permissions) to log into your system. see What userid & password do I need to install Flash Player? for more information