All you have to do is:
1) Multiply the whole numbers:
3*5=15
2) Multiply the Numerators (the top number I'm the fraction):
3*2=6
3) Then multiply the denominators (the bottom number of the fraction):
4*3=12
Then put them all together:
15 6/12
Therefore, 3 3/4 multiplyed by 5 2/3 Is 15 6/12 which can be simplified down to 15 1/2.