Negative inventory quantities

See we are entering a product stock qty. as an example 6. When we billed customer (sales invoice) 2 times 3+3 my stock is 0. But next time if we create invoice on same product with any qty its not showing any message that stock is negative. Manager taking negative entry at that time. Please help me out someone.

That is the way Manager works, and negative quantities indicate a backorder situation. The reason is that some companies sell items before they order or purchase them. Some never take delivery, but have their suppliers drop-ship directly to the end customer.

How i can avoide from negative Qty on hand and Qty Owned and also get average cost , Total Cost ?

It would appear that you have the Goods Receipts and Delivery Notes tabs activated.
If yes, are you using them, that is, are you creating Goods Receipts and Delivery Notes?
If no, then you should de-activate those tabs under Customise.

By definition, average cost cannot exist when you have no quantity on hand. You must resolve the Goods Receipts and Delivery Notes issues first. Average and total costs will appear automatically. So, either enter those transactions or, as @Brucanna suggested, disable the tabs.