The general procedure is to first convert mixed numbers to improper fractions, then to multiply (cancelling numerators and denominators if possible). Final answers are given both in improper form or as a mixed number, depending on how you are typically required to present the final answer in class.
1 7/8 * 4/5 = 15/8 * 4/5 = 3/2 * 1/1 = 3/2 or 1 1/2
7/8 * 3 1/4 = 7/8 * 13/4 = 91/32 or 2 27/32
1 2/3 * 1 1/4 = 5/3 * 5/4 = 25/12 or 2 1/12
3 3/4 * 2 2/5 = 15/4 * 12/5 = 3/1 * 3/1 = 9
6 2/3 * 3 3/10 = 20/3 * 33/10 = 2/1 * 11/1 = 22