4th June, 2002 = (2001 years + Period from 1.1.2002 to 4.6.2002) Odd days in 1600 years = 0 Odd days in 400 years = 0 Odd days in 1 ordinary year = 1 Odd days in 2001 years = (0 + 0 + 1) = 1 Jan. Feb. March April May June = 155 days (31 + 28 + 31 + 30 + 31 + 4) = 22 weeks + 1 day ≡ 1 odd day Total number of odd days = (1 + 1) = 2 ∴ Required day is Tuesday.
Explanation as extracted from the printed page; notation may be imperfect.