ANSWER
8 liters of the first solution and 4 liters of the second solution.
EXPLANATION
The equations that govern the situation have been given as:
[tex]\begin{gathered} A+B=12 \\ 0.8A+0.5B=8.4 \end{gathered}[/tex]
where A represents the amount of the first solution and B represents the amount of the second solution.
From the first equation, we can make A the subject of the formula:
[tex]A=12-B[/tex]
Substitute that into the second equation:
[tex]\begin{gathered} 0.8(12-B)+0.5B=8.4 \\ 9.6-0.8B+0.5B=8.4 \\ \Rightarrow-0.8B+0.5B=8.4-9.6 \\ -0.3B=-1.2 \\ B=\frac{-1.2}{-0.3} \\ B=4L \end{gathered}[/tex]
To find A, substitute the obtained value of B into the equation for A:
[tex]\begin{gathered} A=12-4 \\ A=8L \end{gathered}[/tex]
Hence, you would need 8 liters of the first solution and 4 liters of the second solution.
