I am trying to splice the array on the copy and not original array But looks like the loop ends before it can read the next 6 in the list

It's not the loop ending prematurely, it is wrong indices.

This happens because splice shrinks the array @copy, and after that, the original and copy arrays aren't aligned any more. You need yet another variable which holds the amount of elements spliced off, and decrease $sixindex by that amount at the next splice operation, otherwise the offset is outside the @copy array.

Adding some debug print statements shows the problem:

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dump;
########

 my $aref = [1, 6, 2, 2, 7, 1, 6, 99, 99, 7];
 my $flag = 0;
 my $i = 1;
 my $sixindex = 0;
 my @copy = @$aref;
if (scalar(@$aref) >= 2) {
    foreach my $x (0..$#{$aref}) {
        print "pass $x\n";
        dd $aref;
        dd \@copy;
        if (defined($aref->[$x])) {
               if ($aref->[$x] == 6) {
                 $flag = 1;
                 $sixindex = $x;
                 next;
               }

             if ($flag) {
                   unless ($aref->[$x] == 7) {
                     $i++;
                         next;
                  } elsif ($aref->[$x] == 7 ) {
                         print "splice $sixindex, ",($i+1),"\n";
                         splice(@copy, $sixindex, $i + 1);
                         $flag = 0;
                         $i = 1;
                         $sixindex = 0;
                     next;
              }
          }
      }
    }
}

dd \@copy;
__END__
pass 0
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
pass 1
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
pass 2
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
pass 3
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
pass 4
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
splice 1, 4
pass 5
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 1, 6, 99, 99, 7]
pass 6
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 1, 6, 99, 99, 7]
pass 7
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 1, 6, 99, 99, 7]
pass 8
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 1, 6, 99, 99, 7]
pass 9
[1, 6, 2, 2, 7, 1, 6, 99, 99, 7]
[1, 1, 6, 99, 99, 7]
splice 6, 4
[1, 1, 6, 99, 99, 7]
[download]

The second splice at pass 9 has an offset of 6, but the last element of @copy is at index 5. Pass 4 spliced off 4 elements, so you want offset 2 here (6 - 4).

This does what you want:

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dump;
########

 my $aref = [1, 6, 2, 2, 7, 1, 6, 99, 99, 7];
 my $flag = 0;
 my $i = 1;
 my $sixindex = 0;
 my $spliced = 0;
 my @copy = @$aref;
if (scalar(@$aref) >= 2) {
    foreach my $x (0..$#{$aref}) {
        print "pass $x\n";
        dd $aref;
        dd \@copy;
        if (defined($aref->[$x])) {
               if ($aref->[$x] == 6) {
                 $flag = 1;
                 $sixindex = $x;
                 next;
               }

             if ($flag) {
                   unless ($aref->[$x] == 7) {
                     $i++;
                         next;
                  } elsif ($aref->[$x] == 7 ) {
                         print "splice ",$sixindex-$spliced, " ",($i+1
+),"\n";
                         splice(@copy, $sixindex-$spliced, $i + 1);
                         $spliced += $i + 1;
                         $flag = 0;
                         $i = 1;
                         $sixindex = 0;
                     next;
              }
          }
      }
    }
}

dd \@copy;
[download]

All that indexing stuff is only necessary because you make a copy of the array and delete the ignored elements later. Is that a requirement of the homework? If not, you could drop all that index counting and track keeping stuff, and just push the elements not to be ignored onto @copy :

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dump;
########

my $aref = [1, 6, 2, 2, 7, 1, 6, 99, 99, 7];
my $flag = 0;
my @copy;
if (scalar(@$aref) >= 2) {
    foreach my $x (@$aref) {
        dd $aref;
        dd \@copy;
        if (defined($x)) {
             if ($x == 6) {
                 $flag = 1;
                 next;
             }

             if ($flag) {
                  next unless $x == 7;
                  $flag = 0;
                  next;
             }
             print "push \@copy,$x\n";
             push @copy, $x;
          }
    }
}

dd \@copy;
[download]

The only helper variable left now is $flag. But Perl has the ".." range operator which acts like a flip-flop, and as such has the $flag boolean built-in. Using that:

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dump;
########

my $aref = [1, 6, 2, 2, 7, 1, 6, 99, 99, 7];
my $flag = 0;
my @copy;
if (scalar(@$aref) >= 2) {
    foreach my $x (@$aref) {
        dd $aref;
        dd \@copy;
        if (defined($x)) {
             if ($x == 6 .. $x == 7) {
                 next;
             }
             print "push \@copy,$x\n";
             push @copy, $x;
          }
    }
}

dd \@copy;
[download]

Condense that a bit further, and you have tybalt89's solution.