To calculate this expression, we first need to simplify the fractions:

4/3 x 9/8 x 16/15 x 399

Now, multiply the numerators together and the denominators together:

(4 x 9 x 16 x 399) / (3 x 8 x 15)

Now, calculate the numerator and denominator separately:

Numerator: 4 x 9 x 16 x 399 = 228096
Denominator: 3 x 8 x 15 = 360

Finally, divide the numerator by the denominator:

228096 / 360 = 633.6

Therefore, the result of the expression 4/3 x 9/8 x 16/15 x 399 is 633.6.