OP, Paul is right, you should look up simple questions like this on the web. Also, learn about
different battery chemistrys while you're at it.
AWOL is right - ALWAYS pay heed to the moderators. If you cross them, you're toast. They
never forget, ;-).
C is the capacity of the battery, 4.5 Ah for your case. C/8 is the charging rate = 4.5 Ah/8, in
Amps. AWOL is saying that's a little high, and to reduce it.
"though the adaptor has a selection from 3, 6, 7.5, 9, and 12v...." - this is the voltage out of
your wallwart, not the amperage.
"the 500mA of the charger and the battery has 4Ah, i thought charger must be higher 4ah.." - No,
you use a charging current somewhat less than C, and apply it for some hours to charge the battery.
For example, if you use C/10, or 400 mA, then you would apply this for 11 hours, and it would
move 0.4A * 11 hr = 4.4 Ah of energy into the battery.
But this is all trivial stuff, which you could find on 500 sites by doing a web search.
The one thing the web may not tell you is that a 6V, 300 or 400 mA wallwart will probably charge
your 6V, 4.5 Ah SLA battery fine overnight, without any additional circuitry. This is how many
of the older toys did it, when they still used SLA batteries. For other types, like Nicad, NiMH,
and Li, you need special chargers, and should not use a wallwart directly.
Li batteries, especially, don't like mistreatment,
http://www.businessweek.com/articles/2013-01-18/why-the-batteries-in-boeings-787-are-burning