I'm here to guide you with your Chart of Accounts. 

To begin with, please ensure to choose the correct Billable Expense income account in the Account and Settings.

 Here's how: 

1. Go to the Gear icon. 
2. Navigate to Advanced, then select Chart of Accounts. 
3. From the Billable Expense income account, choose a Billable Expense. 
4. Click Save.

Once done, we can try creating a Bill for the Expense.

1. Click the +New, then select Bill. 
2. Choose the Payee (vendor or supplier).
3. In the Category column, select the appropriate expense account for the transaction.
4. Enter the description and amount of the expense.
5. Check the Billable checkbox.
6. Select the customer you want to bill for this expense.
7. Once done modifying the rest of the field, click Save.

After this, let's link the Billable Expense to an Invoice:

1. Navigate to the Sales page and find the existing invoice.
2. Click on the invoice to expand it.
3. Click the Edit Invoice button.
4. Look for the Balance Due section and click the arrow next to it.
5. Under Add to Invoice, select the billable expense(s) you want to charge your customer.
6. Click Save.

Now, we can open that invoice to check the transaction journal information. This way, we can review if the transaction is correct:

1. Go to Sales, then click the Invoices tab.
2. Open an invoice. 
3. On the invoice screen, click the More button.
4. Select Transaction Journal. 

Additionally, you can turn on the account numbers in your chart of accounts to help you record transactions and organize them by the accounts they affect to help keep the finances organized.

Let me know if you have further queries about managing your chart of accounts or any QuickBooks-related concerns. Keep safe.