TurboTax Online saves your return after each
screen. To exit the program select My Acccount, and Save & Sign-Out. Then proceed to file your extension here: https://turbotax.intuit.com/irs-tax-extensions/
Note: It looks like the browser you are using is Chrome. Some customers that are using
the Chrome browser have encountered an issue where you do not have a drop down from My Account. We are currently unsure of what Chrome setting is causing
it, but TurboTax Online saves your return after each screen in case one were to
get disconnected accidentally. So
you can go a neutral screen where you are not inputting any data, and then
close the browser.
If the problem continues with your Chrome browser, try clearing
your cookies and cache or you can try another browser such as IE or Firefox
(Firefox works best with TurboTax).