(ax)(by)= (ab)(xy)

"Increased by 50%" is the same as itself plus 1/2 iteself or (1+ 1/2) itself = (3/2) itself.

"Decreased by 67%" (you really mean 2/3) is the same as itself minus 2/3 itself or (1- 2/3) itself= (1/3) itself.

You multiplied the first number by 3/2 and multiplied the second number by 1/3. That is the same as multiplying the product by (3/2)(1/3)= 1/2.