The date you will be out of tissues at a rate of two tissues a day, starting January 1st, 2023, is March 1st, 2023. 
The calculation for that goes something like this:

Assuming you have started using the tissue box with 120 tissues total at two tissues a day today, on January 1st, 2023, and we know the most crucial factor, how many days are left in the tissue box's usage, is sixty days, we can begin by subtracting our total remaining days from the days in the current month. There are always thirty-one days in January, the first month of the year, and since our total remaining days surpass the current month, we can safely subtract 31 days from our 60 total days and proceed to calculate for the next month with 29 days left. Performing the same procedure, this time for February, we must consider the edge case that February has an extra day on leap years. So, we use the defining properties of leap years to ascertain if 2023 is a leap year. If a year is evenly divisible by 4, with the exception of end-of-century years which must be divisible by 400, then it is a leap year. 2023 is not an end-of-century year and it is not divisible by 4 since 2023 leaves a remainder of 3 when divided by 4 which is not 0 -- non-end-of-century leap years have a remainder of 0 when divided by 4. On non-leap years, such as 2023, February has precisely 28 days that we can subtract from our current 29 days, leaving only 1 day to carry over to the next month. Now, since the next month after February, that is March, has precisely 31 days, and 31 is larger than 1, we can deduce that our day we will run out of tissues will be in March, and it must be March 1st since that's how many days we have left of the tissue box by the time we get to March.
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