In the first part of this example, you have

(6.63 x 10^{-34} J/Hz) x (2.3 x 10^{16} Hz)

You multiply the numbers:

6.63 x 2.3 = 15

then the exponents. Since you are multiplying, you add the exponents:

(10^{-34}) x (10^{16}) = 10^{(-34 +16)} = 10^{-18}

Thus, the answer is 15 x 10^{-18}, but that is not standard. To make it standard, you must divide 15 by 10 to get 1.5. This means you must multiply 10^{-18} by 10 to get 10^{-17}. The answer, then, is

1.5 x 10^{-17} J

Now, having done all that, if you have a scientific calculator, it allows you to input the numbers in scientific notation and it does all of this for you. If you have a scientific calculator, read the manual to find out how to do this or try to find a demonstration on YouTube.