Q: I shifted the lever to drive mode, but it goes to reverse mode. What is the problem?

You are very nearly right. There is a bowden type cable that connects the the shifter to the transmission. It has adjustable ends and one or more of those adjustments has probably worked loose. That or you might need a new shift cable or new bushings at the connections. Either way, you can have the problem conveniently solved by contacting Your Mechanic. They will send a technician to your home or office to check out your shifter and transmission and tell you exactly what you need to repair it. Meanwhile, be very careful with this car, it might not go into park when you expect it to so be sure to set the brake and park it very carefully.