Even more appropriate for a newbie (because it's less complex and doesn't use regexes) might be:

my @sorted_array = sort {
  # compare the second numbers
  substr($a, 12, 9) <=> substr($b, 12, 9)
  # compare the third numbers
  or substr($a, 22, 12) <=> substr($b, 22, 12)
} @array;
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That is, for each pair of lines that's being compared, use substr to get the fixed fields, and compare them numerically. The first <=> will return non-0 if the numbers in the second field are different, and the third field won't be compared in that case (because of the or).