Someone thinks of a number when he multiplied his number by 5 and subtracts 16 from the result he gets the same answer as when he adds 10 to his number and multiplies that result by 3 finder the number hes thinking of

Let's call his secret number 'M' (for mystery-number).

multiplied it by 5 . . . 5M
subtracted 16 from the result . . . 5M - 16

adds 10 to the number . . . M + 10
multiplies that result by 3 . . .  3(M+10)

Both processes produce the same results:

                                             5M - 16  =  3 (M + 10)

Eliminate parentheses
on the right side:                 5M - 16  =  3M + 30

Subtract  3M 
from each side:                   2M - 16  =           30

Add  16  to each side:        2M          =           46

Divide each side by  2 :        M          =           23