To solve the problem of adding two times in the 24-hour clock format, specifically \(6:30\) and \(19:50\), follow these steps:
Convert the times to minutes: \(6:30\) is \(6 \times 60 + 30 = 390\) minutes. \(19:50\) is \(19 \times 60 + 50 = 1190\) minutes.
Add the total minutes: \(390 + 1190 = 1580\) minutes.
Convert the total minutes back to hours and minutes: First, divide the total minutes by 60 to find the hours: \(\text{hours} = \left\lfloor \frac{1580}{60} \right\rfloor = 26\). Then find the minutes: \(\text{minutes} = 1580 \mod 60 = 20\).
Convert the hours into the 24-hour clock format: Since \(26 \, \text{hours} = 24 + 2\), the time in the 24-hour format is \(2:20\).
So, the correct answer is \(2:20\). This matches the given correct option \(2:20\).