The ram slots are completely different and you cannot put the DDR2 stick in a DDR3 ram slot. When you look at the bottom of the DDR2 ram stick you will notice a space and that lines up with the ram slot and that space is different in the DDR3 stick and slot so that is why you can't use them together. Besides that they are different technology wise as well , a motherboard will either support DDR2 or DDR3 and not both.
DDR3 will not fit into your machine. The RAM will no fit into it's designated slot. They are incompatible and since you already have it, either opt for and upgrade or sell it and by a larger capacity DDR2 stick for the eMachine.
A few motherboards (very rare, none of them new) support both DDR2 and DDR3 but only one type at a time. I will assume your machine doesn't have such a board if it is a prebuilt computer. without dual support a motherboard is locked to one type of memory permanently. The pinout of a DDR2 module and a DDR3 module is logically different and the notches in the pins are different to prevent users from installing the wrong type of memory in the wrong slot. If you did manage to mismatch a module and slot it would not work and probably overheat until it started smoking or caught fire.