The synodic period is the amount of time required for a planet to return to the same point in its orbit relative to the Earth and Sun.
To read more about the synodic period, click here.

1) The planet Venus takes 224.70 days to orbit the Sun and the Earth takes 365.26 days. What is the synodic period of Venus?

Entering 224.70 and 365.26 into the calculator (either number can be SP₁ or SP₂) then clicking "CALCULATE" we find the answer is 583.91 days.

Another definition of synodic period is the time required for a planet to show the same phase again. The planets (except for Venus and Mars) don't show very distinct phases but the Moon definitely does.

2) If the Moon orbits the Earth in 27.321 days relative to the stars, what is the synodic period of the Moon?

Enter 365.26 and 27.321 into the calculator, click "CALCULATE" and your answer is 29.53 days. This means that the Moon takes 29.53 days to go from one full Moon to the next one.