what is theCos B if SinB = 3/4 and Cos A = 1/3 and Sin A = 2 x sqrt 2 over 3?

The ratios for angle A are irrelevant. (there is no relationship mentioned between A and B)

SinB=3/4 (since it is positive, B must be in the 1st or second quadrant)

draw a right angled triangle.

Mark one of the accute angles B  Let the opposite side be 3 unit and the hypotenuse be 4 units.

using pythagoras' theorum

adj side = sqrt(16-9)=sqrt(7) 

CosB=sqrt(7)/4  (if B is in fist quad)

general answer 

$$Cos(B)= \dfrac{\pm \sqrt7}{4}$$