4:00 PM

Hour hand takes a complete rotation of $360^\circ$ in 12 hours i.e 720 minutes. so hour hand traces $\frac {1}{2}^\circ$ in a minute.
Minute hand traces $6^\circ$ in a minute. So, Angular speed of minute hand relative to hour hand is $6-\frac{1}{2}=\frac{11}{2}^\circ$ per minute.
At 4:00 , the angle between the hour and minute hand will be $120^\circ$ . so to overlap, minute hand will have to cover $120^\circ$ relative to hour hand. so time taken to overlap = $\frac{120}{\frac{11}{2}}=\frac{240}{11}=$ 21.81 minutes (approx.) .
Hence, they will overlap 21.81 minutes past 4.

It will come together at 4:20.Since at this time the hour hand at 4 coincides with the another hand and so it appears to be together.

I don't know the solution. maybe some of you know the solution :) it is my assignment in algebra hehehe