We can multiply or divide quantities having different dimensions, however, we cannot do this in case of addition and subtraction. Take a simple example of momentum. Momentum is mass time velocity. Both mass and velocity have different dimensions; [M] and [LT^-1], respectively. However, they are multiplied to get momentum (quantity of motion) of that body. The dimensions of momentum are [MLT^-1].
On the other hand, quantities of different dimensions cannot be added or subtracted. As an example, we cannot subtract time from mass, or add length of the road with the temperature of the surrounding.