def validate_image(layer_list):
    """ 
    Takes list of image layer strings.
    
    Validates image layer data by finding the layer with the fewest 0 digits,
    and then determines and returns the number of 1 digits multiplied by the number
    of 2 digits in that layer.
    """
    
    min_count = 150
    best_layer = -1
    
    for i in range(len(layer_list)):
        zeroes = layer_list[i].count('0')
        if zeroes < min_count:
            min_count = zeroes
            best_layer = i
            
    return layer_list[best_layer].count('1') * layer_list[best_layer].count('2')