my $beg = qr/^\s*APP>\sSTART_PARTU_8X8\n\s*APP>\sPARTITION_SPLIT/;
    my $end = qr/^\s*APP>\sEND_PARTU_8X8/;
    if (/$beg/../$end/){
    print "$line\n";
    }  

##</code><code>##

    APP> START_PARTU_8X8
    APP> PARTITION_NONE
    START_PARTU_16X16
    APP> END_PARTU_8X8

    APP> START_PARTU_8X8
    APP> PARTITION_SPLIT
    START_PARTU_4X4
    ........
    START_PARTU_4X4
    ........
    START_PARTU_4X4
    ........
    START_PARTU_4X4
    ........
    APP> END_PARTU_8X8
    PARTU_16X4
    16X16
    4X16   
    APP> END_PARTU_8X8

##</code><code>##

    APP> START_PARTU_8X8
    APP> PARTITION_SPLIT

##</code><code>##

   APP> END_PARTU_8X8

##</code><code>##

Output:

    START_PARTU_4X4
    START_PARTU_4X4
    START_PARTU_4X4
    START_PARTU_4X4