function to move zeros from a given list to the last

This will make it easier for you to understand and others to read:

Basicly collecting all the nums and the zeros and just adding the lists.

def move_zero(lst):
    zeros = []
    nums = []
    for num in lst:
        if num == 0:
            zeros.append(num)
        else:
            nums.append(num)

    return nums + zeros

print(move_zero([1, 2, 4, 0, 4, 0, 4, 6, 0, 1]))

output:

[1, 2, 4, 4, 4, 6, 1, 0, 0, 0]

What is the problem?

You are removing elements from the list, using list.pop while iterating but you haven't considered the fact that the elements from the list(with a bigger index) have changed index.

How can you approach the solution?

Staying consistent with your code, it would be necessary to subtract the total of elements removed before using the list.pop method.

NOTE: On the function, I put a print function for printing the elements; this is only for debugging purpouses and should be removed in the final code

Code

Here is the code; as stated in the comments, the function is returning None and it's modifying the list in-place.

Also, I converted the for loop at the end, from

for i in range(0,c):
    lst.append(0)

to this code, using generator expression, combined with the list.extend method:

lst.extend(0 for _ in range(c))

Here is the code implementation that i came up with:

def move_zero(lst):
    """
    Given a list of integers, moves all non-zero numbers to the beginning of the list and
    moves all zeros to the end of the list.  This function returns nothing and changes the given list itself.

    For example:
    - After calling move_zero([0,1,0,2,0,3,0,4]), the given list should be [1,2,3,4,0,0,0,0] and the function returns nothing
    - After calling move_zero([0,1,2,0,1]), the given list should be [1,2,1,0,0] and the function returns nothing
    - After calling move_zero([1,2,3,4,5,6,7,8]), the given list should be [1,2,3,4,5,6,7,8] and the function returns nothing
    - After calling move_zero([]), the given list should be [] and the function returns nothing
    """
    c = 0
    for i in range (0,len(lst),1):
        if not lst[i-c]:
            lst.pop(i-c)
            c += 1
    lst.extend(0 for _ in range(c))
    print(lst)

move_zero([1,2,0,3,0])

I would also suggest to iterate over a copy of the list:

def move_zero(lst):
    """
    Given a list of integers, moves all non-zero numbers to the beginning of the list and
    moves all zeros to the end of the list.  This function returns nothing and changes the given list itself.

    For example:
    - After calling move_zero([0,1,0,2,0,3,0,4]), the given list should be [1,2,3,4,0,0,0,0] and the function returns nothing
    - After calling move_zero([0,1,2,0,1]), the given list should be [1,2,1,0,0] and the function returns nothing
    - After calling move_zero([1,2,3,4,5,6,7,8]), the given list should be [1,2,3,4,5,6,7,8] and the function returns nothing
    - After calling move_zero([]), the given list should be [] and the function returns nothing
    """
    c = 0
    for i,x in enumerate(lst.copy()):
        if not x:
            lst.pop(i-c)
            c += 1
    lst.extend(0 for _ in range(c))
    print(lst)

move_zero([1,2,0,3,0])

Output:

[1,2,3,0,0]

def move_zero(lst):
    zeros = []  # a list to store all the zeros
    for num in lst:
        if num == 0:
            zeros.append(0)
            lst.remove(0)  # remove this zero from the list for now
    lst = lst + zeros  # append the zeros to the end of the list
    return lst
print(move_zero([1, 2, 4, 0, 4, 0, 4, 6, 0, 1]))

output: [1, 2, 4, 4, 4, 6, 1, 0, 0, 0]

Not the most efficient way but it will do the job. Hope this helps.