Transmission fluid and coolant mix in a car's engine when the transmission cooler lines are compromised and allow transmission fluid to enter the coolant system. The two fluids mix together and can cause serious damage to the engine if not caught and fixed quickly.
The biggest issue with mixing transmission fluid and coolant is that it can lead to corrosion of metal parts in the engine. The acidic nature of transmission fluid will eat away at metal, causing it to weaken and eventually fail. This can cause all sorts of problems, from leaks to complete engine failure.
If you think your car may have mixed fluids, it's important to get it checked out by a mechanic as soon as possible. They will be able to flush the system and replace any damaged parts, getting your car back on the road safely.