To solve this problem, we need to find the values of sin(a) and cos(a) first.

Given sina = √4/6, we can simplify it as follows:
sina = √(4/6)
sina = √(2/3)
sina = √2/√3
sina = (√2/√3) * (√3/√3)
sina = √6/3

Now, let's find the value of cos(a) using the Pythagorean identity:
cos^2(a) + sin^2(a) = 1
cos^2(a) + (√6/3)^2 = 1
cos^2(a) + 6/9 = 1
cos^2(a) = 1 - 6/9
cos^2(a) = 3/9
cos^2(a) = 1/3
cos(a) = ±√(1/3)
Since sina is positive, we can take the positive value for cos(a):
cos(a) = √(1/3)

Now, let's calculate sin(2a) using the double angle formula:
sin(2a) = 2 * sina * cosa
sin(2a) = 2 * (√6/3) * (√1/3)
sin(2a) = 2 * (√6/3) * (√1/√3)
sin(2a) = 2 * (√6/3) * (√3/3)
sin(2a) = 2 * (√6/3) * (√3/3)
sin(2a) = 2 * (√18/9)
sin(2a) = 2√18/9

Finally, let's calculate sin^2(a) * cos(a):
sin^2(a) * cos(a) = (√6/3)^2 * √(1/3)
sin^2(a) * cos(a) = (6/9) * (√1/√3)
sin^2(a) * cos(a) = (6/9) * (√3/3)
sin^2(a) * cos(a) = 6√3/27
sin^2(a) * cos(a) = √3/9

Therefore, sin(2a) * cos(a) = 2√18/9 * √3/9 = 2√6/9 = √6/9.