This is one way to do it without a hash table. Your grouping constraints can be enforced by sorting the table. then roll through the table doing sums and printing every time the grouping changes.

use strict;
use warnings;
use Data::Dump qw(pp);

use constant { "AcctName" => 0, "EntityName" => 1, "UnitName" => 2};

my @array = (
             ['Account01',    'Entity01',    'Unit01',    1,    2,    
+3],
             ['Account01',    'Entity01',    'Unit01',    4,    5,    
+6],
             ['Account02',    'Entity02',    'Unit02',    10,    11,  
+  12],
             ['Account01',    'Entity01',    'Unit01',    7,    8,    
+9] );

@array = sort {$a->[AcctName] cmp $b->[AcctName]
                              or
               $a->[EntityName] cmp $b->[EntityName]
                                or
               $a->[UnitName] cmp $b->[UnitName] }@array;
pp \@array;   

die "input array too small!!" unless @array>=2;
my $firstRowRef = shift @array;
my @startRow = @$firstRowRef;

foreach my $row_ref (@array)
{
    my @curRow = @$row_ref;
    
    if ($curRow[0] ne $startRow[0] or
        $curRow[1] ne $startRow[1] or
        $curRow[2] ne $startRow[2] )
    {
        print "@startRow\n";  # new grouping
        @startRow = @curRow;
    }
    else                      # group continuation
    {                         # add current month #'s to totals
        $startRow[3]+=$curRow[3];
        $startRow[4]+=$curRow[4];
        $startRow[5]+=$curRow[5];
    }    
}

print "@startRow\n";  # This is for the last row of array           
               
__END__
sorted array is:
[
  ["Account01", "Entity01", "Unit01", 1, 2, 3],
  ["Account01", "Entity01", "Unit01", 4, 5, 6],
  ["Account01", "Entity01", "Unit01", 7, 8, 9],
  ["Account02", "Entity02", "Unit02", 10, 11, 12],
]
Account01 Entity01 Unit01 12 15 18
Account02 Entity02 Unit02 10 11 12
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