Four billion years into the future, the Moon will be about twice the distance to the Earth.  How long will the days be?

The length of a day on Earth is determined by the speed at which it rotates on its axis. This speed is gradually slowing down due to the gravitational interaction between the Earth and the Moon, a process known as tidal friction.

Currently, this process is causing the day to lengthen by about 1.7 milliseconds per century. However, as the Moon moves further away, this process will slow down, so the rate at which the day is lengthening will decrease over time.

If we assume a linear rate of increase, we can estimate the length of a day 4 billion years in the future by multiplying the current rate of increase by the number of centuries in 4 billion years. However, this would be a significant overestimate, because the rate of increase is expected to decrease over time.

A more accurate estimate would require a detailed model of the Earth-Moon system and how it will evolve over time, taking into account factors such as changes in the Earth's shape and internal structure, changes in the Moon's orbit, and the influence of other celestial bodies. This is a complex task that is beyond the scope of this assistant.

However, it's safe to say that the length of a day will be significantly longer than it is now, possibly on the order of 25-30 hours or more. But this is a rough estimate and the actual value could be significantly different.