In the lab, there are two solutions that contain alcohol and Yolanda is mixing them...

Let solution B be V_B
The sum of alcohol in solution A and solution B is equal to the quantity of alcohol in the mixture of solution A and solution B.
Thus, the sum of 12% alcohol in solution A and 40% of alcohol in solution B is equal to the 24% of alcohol in the mixture of solution A and solution B.
$\frac{12}{100}(V_A)+\frac{40}{100}(V_B)=\frac{24}{100}(V_A+V_B)$
Now, substitute the value of $V_A=800ml$ in the equation above:
$\frac{12}{100}(V_A)+\frac{40}{100}(V_B)=\frac{24}{100}(V_A+V_B)$
$\frac{12}{100}(800ml)+\frac{40}{100}(V_B)=\frac{24}{100}(800ml+V_B)$
$96ml+\frac{40}{100}(V_B)=192ml+\frac{24}{100}(V_B)$
$96ml+\frac{40}{100}(V_B)-96ml=192ml+\frac{24}{100}(V_B)-96ml$
$\frac{40}{100}(V_B)=96ml+\frac{24}{100}(V_B)$
$\frac{40}{100}(V_B)-\frac{24}{100}(V_B)=96ml+\frac{24}{100}(V_B)-\frac{24}{100}(V_B)$
$\frac{16}{100}(V_B)=96ml$
$\frac{100}{16}\times \frac{16}{100}(V_B)=\frac{100}{16}\times 96ml$
$V_B=600ml$