unshift is useful for this:

#! perl -slw
use strict;

chomp( my @data = <DATA> );
my $i = 0;
++$i until $data[ $i ] =~ m[Red];
my $saved = $i;
my @desired = $data[ $i ];

for ( 1 .. 4 ) {
    --$i until $data[ $i ] =~ m[White];
    unshift @desired, $data[ $i-- ];
}

--$i until $data[ $i ] =~ m[Blue];
unshift @desired, $data[ $i ];

for ( 1 .. 4 ) {
    ++$saved until $data[ $saved ] =~ m[White];
    push @desired, $data[ $saved++ ];
}

++$saved until $data[ $saved ] =~ m[Blue];
push @desired, $data[ $saved ];

print for @desired;

__DATA__
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