Final answer:
The resolution that women should secure the right to vote was achieved with the ratification of the Nineteenth Amendment in August 1920, which granted American women the right to vote.
Step-by-step explanation:
The resolution's goal that 'it is the duty of the women of this country to secure to themselves their sacred right to the elective franchise' was eventually achieved with the ratification of the Nineteenth Amendment. This amendment came into effect in August 1920, after it was passed by Congress in June 1919. The passage of this amendment prohibited any United States citizen from being denied the right to vote on the basis of sex.
The Nineteenth Amendment was the culmination of a long struggle for women's suffrage, which was marked by divisions and alliances over issues such as race and temperance. Nevertheless, it secured the extension of the right to vote to American women, allowing them to participate in the presidential election of 1920.