If you had an array of file names, and did the following:

    my @grepped = grep /\d{8}\.txt$/ @filenames;
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..then your array @grepped would contain the entry 'file1_system_051117123050.txt' if this filename was in the @filenames array.

However, if you want to capture text from a string, then you want a regular expression match:

    if ( $filename =~ m/(\d{4})\d{4}.txt$/ ) {
        print( $1 . "\n" );
    }
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..if $filename contained 'file1_system_051117123050.txt' then you would have '1712' printed out as that was the four digits captured within parenthesis (curly brackets) in the regular expression match.