Advice in password auto-generation
Only randomly generated components matter for passwords/passphrases.


  6 randomly generated symbols: lower/uppercase letters and numbers.


You have 26+26+10 possible characters, so 62. 

The entropy of a password is $L\log_{2}N$, where $N$ is the number of possible symbols and $L$ is the number of symbols in the password. So you have $6\log_{2}62=35$ bits of entropy. You want a minimum of 80 to be considered reasonably strong.

This is ridiculously weak. For all practical purposes it's a 6-character alphanumeric password.