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AccountRight will allow for the user to enter opening balances for Balance Sheet accounts via Setup>>Balances>>Account Balances. Profit & Loss account opening balances are generally entered via a journal entry. I would recommend speaking to your course provider for further assistance in entering those opening balance and journal entry/entries.
Welcome to the MYOB Community Forum, I hope you find plenty of useful information.
As @Steven_M has mentioned when setting up a new data file from the 1st July you would only need to enter Balance Sheets opening Balances and they are done through Setup > Balances > Account Opening Balances.
If entering Opening Balances for a new data file created at any other time through the year you should still use Setup > Balances > Account Opening Balances and enter both Balance Sheet and Profit and Loss opening balances.
In your case from looking at the date of Trial Balance provided, you are creating a new data file to start from the 1st June.
However you also MUST enter the individual transactions for the Trade Creditors and Trade Debtors to Balance back to the opening Balances. this would need to be done even if you entered the Opening Balances as a Journal.
When entering a journal you MUST NEVER enter anything against any of the control accounts otherwise tha balance in the MYOB will be out. Your Control accounts include Trade Creditors , Trade Debtors, Bank and Credit Card accounts, GST accounts and wages account.