Answer
$R_1=18\Omega;R_2=62\Omega$
Work Step by Step
We can find the required resistances of the two resistors as follows:
Given that both resistors are in series
so $R_1=\frac{2.7V}{0.15A}=18\Omega$
Now the equivalent resistance is
$R_{eq}=R_1+R_2$
$\implies \frac{V}{I}=R_1+R_2$
$\implies R_2=\frac{V}{I}-R_1$
We plug in the known values to obtain:
$R_2=\frac{12V}{0.15A}-18\Omega$
$R_2=62\Omega$