New to leases need some help

Hello there! I am new to the forum but have been reading posts to get an idea of how leases work. I am in the market for a 36-48 month lease with 10-12k a year. My situation is the following, I am negative on my car loan. I owe 13000 with my car being worth 6k max. I am looking to see how i can roll that much into a lease with a max monthly of $350. Is this feasible? I do not have a car preference and am open to compacts to suv. I was wondering if you guys can help me brainstorm my situation. I have 2k to put down. Please let me here your ideas. Thank You!