I went to target tonight to purchase a few items. My subtotatal before coupons was $22.59, and after coupons my subtotal was $ 2.81. The question I  I have is why is tax charged on the larger amount, and not the after coupon amount. I double checked at the service desk, and they said thats just how it's supposed to be? So I was charged $1.36 in tak, instead of $0.16 in tax. Is that correct?

In most states, state law requires that tax is charged on the subtotal before coupons are added. (some stores don't print receipts until after, so the coupons may show with the product and not at the bottom, but are still calculated after the subtotal). The only way to legally "get out of" paying full tax is to go to a store like Walmart or Target that allows overage with a coupon large enough to cover the taxes and the product. For example, the $1/1 J&J coupons used at Walmart for the $.97 travel kits means .97 of the coupon goes to the product and .03 goes toward taxes. But in the end, Walmart still pays the tax on the full price to the government, and gets the full coupon price from the manufacturer, so everyone's happy!