So I will try and make this simple and easy! I currently have an auto loan through Santander Consumer USA for org $18,299 I have paid it down to $15,892 it is worth trade in at dealership between 11,500-12,000. I saw a car I would like to trade for that is $19,140. I applied for a new loan through road loans and got approved for $16,582 with 4500 down. Can I use my car trade in value as down payment of 4,500. So if I am doing the math correctly I owe 15,892 and it's worth lets say 12,000 leaving $-3,892 to go onto new car loan. so new car $19,140-$12,000(my car value)=$7,140+$3,892(car negative value to cover)=new amount financed $11,032 is this correct or am I missing something here. I am also aware with financing I will pay more but I want to make sure this is the amount to be financed. Please help 
So mathematically you created money. 
Think about it: you have an underwater car. You're buying another car. Logically how can you owe less than the purchase price of the new car on the new loan?
You forgot that the 12k from your car has to be used to pay off the 15k loan on it. Here's how the math is going to go:
19,140 (purchase price of new car)
+3,892 (underwater)
--------------------------------
23,122 (new loan amount) - down payment in cash
If you insist, I can throw your other #'s in to show you what you forgot (but Roadloans does not see the math this way per se):
19,140 (purch price)
+15,892 (current loan to be paid off)
-12,000 (trade in value)
---------------------------------------
23,122 (new loan amount)
So no. You will not be able to buy what you are proposing unless you bring ~ 23k-16.5k=6.5k in CASH with you. Also you can't count your trade as dp when it's underwater. Even if it weren't underwater, some loans do not allow you to count trade positive equity as dp, though most will allow it if you have positive equity.
Now let's see what we CAN do to help you buy that car. How about giving me this info here:
Credit Score (bureau(s)?):
AAoA:
# of positive trade lines:
# of negative trade lines:
Income before any taxes are taken out:
Lenght of Employment:
Previous Loan Experience:
Monthly rent/mortgage:
Monthly aggregate minimum payments across all credit cards:
Any other loans (other than the rent/mortgage and credit cards discussed above):
Year of Car:
Miles:
Purchase/Refinance:
Requested loan term (XX Months):
Down payment amount:
Co-borrower/Co-Signer:
Other:
Finally, what APR did Roadloans give you for the current approval?