In a small saucepan combine the sugar and 3/4 cup water. Bring to a simmer, stirring to dissolve the sugar. Cool.
For each drink, place 6 mint leaves in the bottom of a 10 to 12 ounce glass. Add 2 tablespoons of the sugar syrup plus 1 tablespoon each of the lime juice and rum or tequila. Crush (muddle) the mint into the liquid with a muddler or the back of a spoon or fork to release its flavor. Fill the glass about 3/4 full with ice cubes. Slowly pour in half of one of the beers, stir well with a long-handled spoon and serve right away.