To address the actual question: It's not entirely clear what you want the code to do. What do you want the output to look like?

hence @p will be 4D

I re-wrote your code as shown below. As I think you understand, if you want 9,7 or 3.4 to be grouped together, you need to put those into an anonymous array and put the reference to that array into the simple list, @l. That's what my @l=([9,7],[3,4]); does.

Now to add FOO to @l, you don't need to repackage @l, @l is already a list of references to array (a list of perhaps 2D coordinates). push @p,['FOO',@l]; is the same as push @p,['FOO',[9,7],[3,4]]; I removed the () in the args to push because most of the time, Perl built in functions don't require them.

After the 2nd push, we now have array p which contains, 2 "units" that each consist of a name and some number of 2D coordinates. If we want to get rid of FOO, we have to "unpackage" or dereference and extract the individual elements of that "unit". Now, the first one can be thrown away. Then we have to "repackage" the elements into a new anon array ref and pass that modified "unit" to @p @new.

Often in practice, it works out better to package FOO into an anon array even though that is not strictly required. The reason for this is to make every thing in the "unit" the same. I showed that and that making a flat list is now easy because ['FOO'] looks more like one of the coordinates [9,7]. And there is not "if" logic required to skip de-referencing a simple string.

use strict;
use warnings;
use Data::Dump qw(dump dd);


my @p=();
my @l=([9,7],[3,4]); # array of 2 coodinates

push @p,['FOO',@l];   # array with the string FOO with those coordinat
+es
push @p,['BAR',[8,0]];# BAR and one coordinate 

dump \@p;  #[["FOO", [9, 7], [3, 4]], ["BAR", [8, 0]]]
           #note outermost brackets are artifact of way we called dump
+ as
           #a reference to an array

# throw away FOO and BAR
#
my @new =map{my @elements = @$_;  #This gets "FOO", [9, 7], [3, 4]
             shift @elements;     #throw away FOO
             [@elements]}@p;      #repackage array inside of brackets
                                  #back to being a reference to array

dump \@new ; # [[[9, 7], [3, 4]], [[8, 0]]]

# often it is convienent to make all elements to the structure the sam
+e
# here packaging the string foo as a single element of an array ref is
+ fine.

my @x;
push @x,[['FOO'],@l];   # array with the string FOO with those coordin
+ates
push @x,[['BAR'],[8,0]];# BAR and one coordinate 

my @flat = map{@$_}map{@$_}@x;
print "@flat\n"; # FOO 9 7 3 4 BAR 8 0
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