To hinder something would be to make it more difficult to accomplish. In your sentence, whatever "it" is would make it more difficult for the government to achieve the goal of quality education. For example, not having enough money to pay good teachers could make it more difficult for the government to provide quality education. I would add a definite article before "government" in your sentence: "In addition, it will hinder the government's goal of providing equal and quality education to all children."