How can I run a report that gives me the detailed automobile expenses for this year in new QuickBooks Online?

Run Transaction Detail by Account and customize the report to show just Automobile Expense account.
Select the blue navigation bar on the left

This report will show all transaction details by all accounts
We will to need to customize this report just to show Automobile Expense account only.

Change Transaction date as necessary (for example change to This Year to run report this year only)
Click Customize button (located top left corner)
Select “Lists”
Go to Distribution Account under Lists
Scroll down the list and select “Automobile Expense”
Select Run Report button
Now you’ve Transaction Detail by Account report for Automobile Expense account only.
If you need to run similar report for other accounts, follow the same steps, just select appropriate account from Distribution Account List.

You can also customize this report (click Save Customizations button) if you need to see just Automobile Expense next time.

Run Transaction Detail by Account and customize the report to show just Automobile Expense account.

Other way to generate that report is to use your chart of accounts to create a “QuickReport.”

To do this:

Click on the gear in the top right and choose “Chart of Accounts” in the dropdown
On the chart of accounts, scroll down to the expense account you categorized your interest to
Click on that account once and then click the “Report” button in the upper right
Set your date range at the top of the report and click the “Run Report” button and you’re good to go!