How do you interpret this:
"Billed Rio Company 6,000 for services performed. A 50% down payment was received."

- Where am I going to put it in a t account? What I am planning to do is to debit 6000 on acc. Receivable then after that I don't know anymore what to do next. Hehe. Im confused with the down payment

Services performed means you provided a service to a customer so you have Service Revenue. The amount is 6,000 and received 50% down payment. This means that you billed a customer 6,000 for a service you provided and you received 50% in cash or 3,000 which means the customer still owes you 3,000. So your accounts will be Cash for the cash received and Accounts Receivable for the amount the customer owes you.

Now your journal entry will be:
Debit Cash for 3,000 (this is the 50% down payment from the 6,000 billed)
Debit Accounts Receivable for 3,000(this is the amount the customer owes you from the 6,000 bill)
Credit Service Revenue for 6,000 (this is the total amount of service provided to a customer.

Note. You have two debits of 3,000 which equals 6,000 and you have a credit for 6,000. This means your journal entry balances because your debits and credits equal 6,000.

Thank you so much for your help! =))))

Can I ask another question? What if this is the problem:

"signed a contract of lease for a monthly rental 10000"

There is no journal entry required. The company signed a legal document to pay 10,000 a month in rent.

The only time it will matter in a homework problem is when you have a problem where you have adjusting entries like in an accounting cycle or are preparing financial statements for a partial or whole year.

Based on the statement above the company would pay rent at the beginning or the end of each month. Your journal entry when the rent is paid at the end of the month is:
Debit Rent Expense for the amount paid
Credit Cash for the amount paid

Beginning of the month:
Debit Prepaid Rent for the amount paid
Credit Cash for the amount paid

At the end of the month you will have an adjusting entry for Prepaid accounts. The adjusting entry will be:
Debit Rent Expense for the amount of rent used in the month(or number of months used in the accounting period)
Credit Prepaid Rent for the same amount
Note: This entry transfers the amount of rent that has been paid in advance of use to an expense account, thereby following the US GAAP Matching Principle which matches expenses to the period in which they are incurred and revenues to the period they are earned.