I have 13.5 VDC output, and i want to power up a small radio that takes 4.5 VDC. I thought about adding 5/6 used 1.5V batteries in series, so it would be about 4.5 VDC for radio and about 8 VDC for batteries. Would that "battery voltage reducer" work? If not, how can i reduce voltage without using any complicated electronical stuff? (I am not an electrician)
Your battery solution will not work and may be dangerous.
You need something like this; (search for "dc dc converter"; anything car orientated will be suitable, given that car battery voltage is somewhere in the 12-15V range)
You said "small" radio, but didn't say how much current it draws. If only a little, a 7805 voltage regulator may be all you need. Does the radio actually say on it that it needs 4.5V, are you getting this from the fact that it takes 3 1.5V cells, or something else? If this is battery operated, then most likely it will work fine on 5 volts. If you are worried about the exact voltage, use a adjustable regulator to make 4.5V.
Keep in mind that a linear regulator dissipates the difference in voltage times the current as heat. If the radio draws 100 mA, for example, then a 5V linear regulator would dissipate 850 mW. That's about the limit for a TO-220 package standing up from the board in free air. Put even a small heat sink on it and it should be fine. If the radio draws only 50 mA, then just a bare 7805 in TO-220 package is all you need. If 200 mA, then you should start to seriously consider a switching regulator.
Something like linear voltage regulator 7805 probably will be excellent for your case as it is very cheap, very simple to use, you need only 2 very cheap capacitors (something in the range from 22pF - 100nF will be OK for you) for "just in case" smoothing and optionally but highly recommended one rectifying diode as 1N4007 before 7805. You don't need a heat-sink for 7805 with 13-14 volt input. This setup will provide you with arguably the cheapest solution (bill of materials wise) and most simplistic one. Unused power will be dissipated as heat but it will be negligible and you shouldn't feel it.
P.S. I will edit my post little bit later to provide you with schematic to use.
The problem with using the batteries is that they will always be charging. Draw it out and notice how current will enter the positive terminal of the battery. That's opposite to the way batteries are usually used and means the battery is charging, instead of supplying. Always charging means the batteries will eventually pop.
Unfortunately, to convert voltages you need complicated electronic stuff. The simplest solution is the linear regulator others have mentioned. It's almost as simple at your battery solution (one lead goes to the source and one goes to the battery). The only difference is that there is a third lead which needs to go to ground. Depending on how hungry your radio is, it also may get (too) hot, but that's electronics for you...