How do I tell my boss that she either has to approve my 4 months notice or accept my 2 weeks resignation?

Basically I’m a university age (18y.o.) employee for a major grocery store chain in Australia and have planned (and booked) a vacation with a large group of my friends to Vietnam in December. When I submitted my leave (4 months notice) it was instantly declined which lead to the attached text conversation. I enjoy working at this place but want to live my life and be able to take leave whenever I can to see the world. As the title says, how can I tell my boss to accept my 4 months holiday notice?