The month's total wages paid June amounted to $7,390. The employees worked twenty-one days but were paid for only twenty days because for the day worked is the next pay period. How do I come up with the correct amount? Which is 369.50

You will do an adjusting entry for the one day.
The journal entry to record this is:
Debit Wage Expense for the amount
Credit Wages Payable for the amount

When you pay the wages in the next period you will:
Debit Wages Expense for the amount of wages during the period
Debit Wages Payable for the amount in the account
Credit Cash for the total amount.

The 7390 that was paid covered 20 days, so you just divide by 20 to get one day's worth.