### Step-by-Step Solution
Part (a): Rewrite each number in standard notation.
We start by converting the numbers from scientific notation to standard notation.
1. [tex]\(6.0 \times 10^{-3}\)[/tex]
[tex]\[
6.0 \times 10^{-3} = 0.006
\][/tex]
2. [tex]\(4.00 \times 10^{-6}\)[/tex]
[tex]\[
4.00 \times 10^{-6} = 0.000004
\][/tex]
So, in standard notation, the numbers are:
[tex]\[ 6.0 \times 10^{-3} = 0.006 \][/tex]
[tex]\[ 4.00 \times 10^{-6} = 0.000004 \][/tex]
Part (b): Calculate the answer.
Next, we multiply these two numbers.
[tex]\[
0.006 \times 0.000004
\][/tex]
Performing the multiplication:
[tex]\[
0.006 \times 0.000004 = 2.4 \times 10^{-8}
\][/tex]
To present our answer in scientific notation, we ensure it is rounded to one decimal place if necessary:
[tex]\[
2.4 \times 10^{-8}
\][/tex]
Thus, our final result in scientific notation is:
[tex]\[
\boxed{2.4 \times 10^{-8}}
\][/tex]
