17^th June, 1998 = 1997 years + Period from 1.1.1998 to 17.6.1998

Odd days in 1600 years = 0

Odd days in 300 years = $\left(5 \times 3\right)$ $\equiv$ 1

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years $\left( 24 \times 2 + 73\right)$ = 121 = 2 odd days.