If Saturday falls four days after today which is 6th January, on which

We need to find the day of the week for 1st December of the previous year.
Let the current year be Y. We are finding the day of 1st December, Y-1.
The period is from 1st December, Y-1 to 6th January, Y.
Number of days in December Y-1 = 31 days.
Number of days in January Y up to 6th = 6 days.
Total number of days = 31 + 6 = 37 days.

To find the day of the week 37 days before Tuesday, we find the number of odd days in 37.
Number of odd days = $37 \pmod 7$.
$37 = 5 \times 7 + 2$. The remainder is 2.
So, 37 days is equal to 5 weeks and 2 days.
The day of 1st December, Y-1 is 2 days before Tuesday.
Tuesday – 1 day = Monday.
Monday – 1 day = Sunday.