How many times do the hands of a clock point towards each other in a day?

$A$ girl was born on September $6, 1970$,which happened to be a Sunday. Her birthday would have fallen again on a Sunday in:

$A$ wall clock gains $2$ minutes in $12$ hours,while a table clock loses $2$ minutes every $36$ hours. Both are set right at $12$ noon on Tuesday. The correct time when both show the same time next would be

Between $1$ hour and $12$ hours,how many times will the hour hand and minute hand be together? (in times)

$A$ clock gains $10$ minutes in every $24$ hours. It is set right on Monday at $8$ am. What will be the correct time on the following Wednesday,when the watch indicates $6$ pm?

At what time are the hands of a clock together between $6$ and $7$?