The best way to multiply complicated problems mentally* is to break them into chunks.
Start with 20 times 8 to get 160, and then 8 times 5 to get 40. Add these together to get 200. 200 times 3 is 600, and 20 times 200 is 4000. Add these together to get your final answer, 4600.
In other words 8 x 20 + 8 x 5 = 200 200 x 3 + 200 x 20 = 4600
*I assumed you meant mentally, because otherwise you'd just multiply longhand, multiplying two of the three numbers and then multiplying their product with the third.
