I came up with:

def ducks_and_dogs(heads=0, feet=0):
    solutions = []
    if feet != 0 and feet % 2 == 0:
        solutions = [
            (ducks, dogs)
            for ducks in range(heads) for dogs in range(heads)
            if ducks + dogs == heads and ducks * 2 + dogs * 4 == feet
        ]
        if solutions:
            for solution in solutions:
                print('{} heads and {} feet could be from {} ducks and {} dogs'.
                      format(heads, feet, solution[0], solution[1]))
        else:
            print('{} heads and {} feet has zero solutions'.format(heads, feet))
    else:
        print('{} heads and {} feet should not happen'.format(heads, feet))

def main():
    tests = [
        {'heads': 45, 'feet': 122},
        {'heads': 74, 'feet': 177},
        {'heads': 12, 'feet': 8},
    ]
    [ducks_and_dogs(**test) for test in tests]

main()

You should have enough there to write your own solution.