Solution

Total execution time is

$100$ seconds

Time taken by multiplication operation is

$80$ seconds

Time taken by other operations is

$100-80=20$ seconds

Now, the program is required to run $4$ times faster.

So, new execution time should be

$\dfrac{100}{4}=25$ seconds

Other operations still take

$20$ seconds

So, time left for multiplication operation is

$25-20=5$ seconds

Originally multiplication operation takes

$80$ seconds

Now it should take

$5$ seconds

So, required improvement in multiplication speed is

$\dfrac{80}{5}=16$

Hence, multiplication operation must be improved by $16$ times.