Dividing by a quarter is the same as multiplying by 4. A better word problem might be 'Kayla and her 3 friends made some brownies, these were shared equally between all 4 of them, giving Kayla 3/2 brownies. How many brownies were originally made?'
Since dividing by 1/4 is the same as multiplying by 4, the number of brownies originally made would be:
3/2 * 4 = 12/2 = 6