thank you for your reply. i have built lm1875 amplifier which uses -18v GND +18v supply. tested amplifier using center tapped transformer.
i can get +18v from battery using lm2577 but how to get -ve voltage from battery?
You can use a buck-boost converter to obtain a negative polarity from the battery. It will give you -18V from +6V.
With the +18V coming from the LM2577, you will get the bipolar supply you plan.
The buckboost may need a different IC. (The LM2577 is described as a boost converter control IC.)
You might prefer to do it all in one circuit. Run the 6V through a full H-bridge to get AC square waves, then through a step-up transformer with center tap. (18-0-18). From there you use diodes and capacitors to obtain the +18/-18 V bipolar supply.
also how to calculate in how much time battery would be discharged?
In raw math, to make the battery last 4 hrs as you plan...
You will draw 6 W average. (Since your battery is 6V, 4.5 A-hrs. That makes 27 watt-hrs.)
6W into an 8 ohm speaker is 6.9 V at .87 A. That should fill a room. The peaks may or may not extend to the rails of a +18/-18 supply.
Now if you decide to draw 12 W average, then your battery will last 2 hrs.
Then, 12 W into an 8 ohm speaker is 9.8 V at 1.2 A.
Or if you decide to draw 24 W average, your battery will last 1 hr.
24 W into an 8 ohm speaker is 13.9 V at 1.7 A.
It all depends on (a) how much volume you want from the speaker, and (b) how long you will operate it, and (c) how much distortion you can tolerate, and (c) how much power the battery can provide.