You've misunderstood. Here's the actual code with our suggested edits:

foreach (@test_node_list) {
    if (-e "/usr/adm/best1_default/collect/$_/noInstance") { # It prob
+ably is a node with data
        if (-e "/usr/adm/best1_default/manager/$_") {        # It has 
+a vis files directory
            push @node_list, $_;
            print "/usr/adm/best1_default/manager/$_/$vis_year$vis_mon
+th$vis_zero$vis_day*.vis";
            if (-e "/usr/adm/best1_default/manager/$_/$vis_year$vis_mo
+nth$vis_zero$vis_day*.vis") {
                system("/appl/perform/best1home/perl/clean_graphics.pl
+", "$_");
                print "It exists.\n";
            }
        }
     }
}
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