My reasoning:

Number of 6-character alphanumeric passwords: (2*26+10)**6 == 56800235584

Number of seconds in a year: 60*60*24*365 == 31536000

Number of years to enumerate all 6-character alphanumeric passwords at one password a second:

  >>> ((2*26+10)**6)/(60*60*24*365)
  1801.1236549974633

(this assumes that alphanumeric is [a-zA-Z0-9], which some might disagree with)