The number of times the hour-hand and the minute-hand of a clock form a right angle (90 degrees) in a day is calculated by the way the hands of a clock move.

Option 1: 44 - This is the correct answer. Within an hour, the two hands form two right angles on most occasions. However, when the time changes from 2 o`clock to 4 o`clock and from 8 o`clock to 10 o`clock, they form a right angle only once. Excluding these four single occurrences, for the other 20 hours they form two right angles each, for a total of 40 occurrences. Adding those 4 single occurrences gives 44 times a day.

Option 2: 48 - This option is incorrect, as it implies that the hands are at right angles twice every hour, which isn`t correct as explained above.

Option 3: 24 - This would suggest the hands create a right angle only once per hour, which is also incorrect.

Option 4: 12 - This would suggest the hands create a right angle only once every two hours, which isn`t the case.