ANSWER
[tex]\begin{equation*} 18.67\text{ cm} \end{equation*}[/tex]EXPLANATION
Parameters given:
Object distance, u = -84 cm
Image distance, v = 24 cm
To find the focal length, apply the formula for focal length for a converging lens:
[tex]\frac{1}{f}=\frac{1}{v}-\frac{1}{u}[/tex]Therefore, the focal length of the lens is:
[tex]\begin{gathered} \frac{1}{f}=\frac{1}{24}-\frac{1}{-84}=\frac{1}{24}+\frac{1}{84} \\ \\ \frac{1}{f}=\frac{7+2}{168}=\frac{9}{168} \\ \\ f=\frac{168}{9} \\ \\ f=18.67\text{ cm} \end{gathered}[/tex]That is the answer.
