How long until my eMMC is dead?
The optimistic estimation would be based on the assumption that your system accumulates data until it can fill one complete erase block, then writes all the data in one go. In that case, your eMMC will live

4'000'000 * 3'000 / (4*20) = 150'000'000 seconds


That's about 4.75 years.

However, if for example your system writes each 4K block separately, the time your eMMC will last will depend on the size of a single erase block. You'll have to check the spec for the actual value, but to give you an example, if your eMMC has 4M erase blocks, you'll have to divide the time by 1024 (meaning it will last just about a day or two).

The real value will be between these two numbers, depending on how you group write operations and how big erase blocks really are.