Your explanation is correct but your example is wrong.
If you have four fouls in the quarter, then you don’t have any fouls to give. The next foul (the fifth foul) will result in free throws
If you have three fouls, then you have a foul to give, because the next foul (the fourth) will not result in free throws.
Note than you start the quarter with four fouls to give (fifth foul is the bonus penalty).
Also note that you cannot have more than one foul to give in the final two minutes of the quarter.
Your explanation is correct but your example is wrong.
If you have four fouls in the quarter, then you don’t have any fouls to give. The next foul (the fifth foul) will result in free throws
If you have three fouls, then you have a foul to give, because the next foul (the fourth) will not result in free throws.
Note than you start the quarter with four fouls to give (fifth foul is the bonus penalty).
Also note that you cannot have more than one foul to give in the final two minutes of the quarter.