def METHOD_NAME(filepath):
    """
    Extracts, cleans, and melts data from the specified Excel file tailored for average years of education by country.
    Parameters:
    - filepath (str): Absolute path to the Excel file.
    Returns:
    - DataFrame: A melted DataFrame after cleaning.
    """
    data_frame = read_excel_data(filepath, "average_years_education_countries")
    cleaned_data_frame = data_frame.dropna(axis=1, how="all").reset_index(drop=True).iloc[:19, :]
    melted_data_frame = cleaned_data_frame.melt(
        id_vars=[cleaned_data_frame.columns[0]], var_name="country_or_region", value_name="average_years_of_education"
    )
    melted_data_frame.rename(columns={melted_data_frame.columns[0]: "year"}, inplace=True)
    melted_data_frame["year"] = melted_data_frame["year"].astype("int64")
    return melted_data_frame