Other monks have explained where the undef values are coming from, but have not explained why your program still works despite the warnings. Since you were honest about this being a homework assignment, I will take some time to explain.

Your program works anyway because neither of the elements in @drop are undef, and while undef eq undef (with two warnings) in Perl, undef ne $string if $string is a defined true value.

Here is the contents of the @colors array on each iteration of the loop, both before and after an element is possibly removed. The element that $num refers to is underlined.

0: before: red green blue yellow pink purple brown
0:  after: red green blue yellow pink purple brown
--
1: before: red green blue yellow pink purple brown
1:  after: red green blue yellow pink purple brown
--
2: before: red green blue yellow pink purple brown
2:  after: red green blue yellow pink purple brown
--
3: before: red green blue yellow pink purple brown
3:  after: red green blue yellow pink purple brown
--
4: before: red green blue yellow pink purple brown
4:  after: red green blue yellow purple brown
--
5: before: red green blue yellow purple brown
5:  after: red green blue yellow purple
--
6: before: red green blue yellow purple
6:  after: red green blue yellow purple
--

I modified the code slightly to print that. While I cannot show you exactly what I used without giving away an answer that you should find, this code shows what the "before" and "after" parts mean:

my @colors = qw(red green blue yellow pink purple brown);
my $count = @colors;
my @drop = qw(pink brown);
my $num = 0;
foreach $num (1..$count){
    $num--;
    print $num, ": before: @colors\n";
    if ($colors[$num] eq $drop[0] or $colors[$num] eq $drop[1]){
        splice (@colors, $num, 1);
    }
    print $num, ":  after: @colors\n--\n";
}
print "@colors \n";
[download]

This technique of inserting additional output to show a program's intermediate states is commonly known as "printf debugging", after the common output function in the C programming language. Perl also has printf, but print is far more commonly used.

The bug in your code that haukex mentioned should be easy to see now, and I will give a few hints towards the "two lines of code" that haukex mentioned:

1. How do you construct a hash from a list in Perl?
2. How can you use map to construct such a list?
3. How do you test for the existence of a hash key?
4. What does grep do in Perl?

And another issue:

5. How can you avoid the wasted seventh iteration of the loop? (Hint: What are the loop control operators in Perl?)

Good luck on your adventures in learning Perl.

Edited 2019-08-18 by jcb: Fix logical error pointed out by haukex: undef is not special under eq and stringifies to an empty string.