We have add 1 2/3 to 1/4. First we have to convert 1 2/3 from mixed number to an improper fraction.
Doing so, we have:

Then, we add the last result to 1/4:

Finally, we convert 23/12 to a mixed number.
Quotient of 23/12 = 1
Remainder of 23/12=11
23/12 as a mixed number is 1 11/12
The answer is the second option.