(log3 2+log9 2)*(log4 3+log8 3)
=(lg2/lg3+lg2/lg9)*(lg3/lg4+lg3/lg8)
=(lg2/lg3+lg2/2lg3)*(lg3/2lg2+lg3/3lg2
=3/2*lg2/lg3*5/6*lg3/lg2
=3/2*5/6=5/4