hey man, lemme try and help you.
OHM = the resistance the electricity has when passing through ANY object. think of water through a pipe - relate it to 'water pressure\resistance'
alrighty then, now that we got that out of the way, if you know anything about magnets, you will have heard of an electro magnet. basicaly, a speaker is a regular slug of a magnet, and an electromagnet - in speaker terms - the electromagnet is called a voice coil.
the voice coil is made of copper wire wrapped around a 'former' or in lamens terms - a tube of heat resistant and very rigid materal (usually kapton, or aluminum). this wire is hooked DIRECTELY to the little terminals you hook the amplifier to on the speaker via little wires called 'tinsel leads'.
now, the 4ohm+4ohm (in a nutshell) means that the voice coil has TWO wires wrapped around it, and the electricity passing through it has a resistance of 4ohms. this can also be labeled as "Dual 4ohm Voice Coil" or "DVC4".
type-r series subwoofer is just that- a brand\model of subwoofer - this particualr model will take a few hundred watts (300~500 depending on the kind of enclosure it is in) and is a low-mid entry level product made by alpine.
RMS basically is the "rated max power" - now - dont ask me why the hell its RMS - because truthfully i dont know //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif
"peak" means that for a fraction of a second, that product can produce or use that amount of power without physically breaking or melting. this is ONLY market HYPE! do NOT buy ANYTHING that does NOT label its "RMS POWER @ [ohm]"
depending on the speakers you choose and the voice coil configuration (in your example, DVC4) you will pick your amplifier.
this is a site where you can put in the voice coil configuration and it will tell you how those speakers can ONLY be wired, in your DVC4 example, you can ONLY wire it to 8ohms or 2ohms... UNLESS there is MORE than one speaker involved. multi-voice coil subwoofers are simply better (in some applications) because of the flexibility of wiring in multiple options.
http://www.rockfordfosgate.com/rftech/wiringwizard.asp
and to let you know, class AB amplifiers that are 2 channel can usually be bridged (using both channels on one speaker) to ONLY 4ohm or they will break, and these amplifiers can be like 400~500w and be under $100shipped. if you are in the market for a pair of 12's and an amp, i would seriously look into this;
http://www.caraudio.com/vb/showthread.php?t=93062
and then two of those Dual 4ohm Alpine Type-R speakers would work PERFECTLY wired like this;
get somone to make box plans for you (maybe $10) on the boards (mmray, ngsm13, inhumanacura, me - but i dont have the time ATM) and build the box yourself. get a 8 or 4 guage wire kit from walmart ($20~25) and ask more questions //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif
but use the SEARCH function in the top black menu bar first. im almost posative most of your questions can be awnsered there //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif
oh yea...
http://www.bcae1.com - TONS of fecking info, this site can awnser every question you have had so far, just look up OHM in the right column.
http://electronics.howstuffworks.com/speaker.htm - how speakers work
read the second one, lots of cool stufF!
hope i helped //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif