The 2-digit number can be represented by 10a+b.
a+b=6, ab=⅓(10a+b)=⅓(10a+6-a)=⅓(9a+6)=3a+2.
So, ab=3a+2, b=3+2/a and a+3+2/a=6,
a2+3a+2=6a, a2-3a+2=0=(a-2)(a-1), so a=2 and b=4; or a=1 and b=5.
The number is 15 or 24. The sum of the digits is 6 in each case. 1×5=15/3; 2×4=24/3.