You could build an array of HTML table cell fragments, and then iterate through 12 elements of the array. Each row will begin at index % 3 == 0, and end at index % 3 == 2.

# --- push everything into an array ---
my @match = ();
foreach my $line (@array) {
    if ($line =~ /\Q$search\E/i) {
        my ($category,$item_name,$item_price,$item_picture)
            = split /\|/, $line;
        push @match, <<End_of_line;
<td valign=top CLASS=MENU1>
  <img src="$photo_loc/$photo1" width=75 height=75><BR>
  <B>$item_name</B><BR>
  $item_price<BR>
</td>
End_of_line
    }
}


# --- Print the table ---
my $inrow;
print "<table>\n";
for (0..11) { # want 12 images
    $cell = shift(@match) or last;
    $inrow++, print "<tr>" if ($_ % 3) == 0;
    print "$cell";
    $inrow--, print "</tr>\n" if ($_ % 3) == 2;
}
print "</tr>\n" if $inrow;
print "</table>\n";
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