The problem provides determinants for two 3x3 matrices and asks for the determinants of two additional matrices. Let's go through this step-by-step.

Given Information

1. $\det \begin{bmatrix} a & 1 & d \\ b & 1 & e \\ c & 1 & f \end{bmatrix} = -5$
2. $\det \begin{bmatrix} a & 1 & d \\ b & 2 & e \\ c & 3 & f \end{bmatrix} = 4$

Step 1: First Determinant

To find the determinant of $\begin{bmatrix} a & 9 & d \\ b & 9 & e \\ c & 9 & f \end{bmatrix}$:

Observe that each element in the second column is now 9. Since adding a multiple of one row to another row does not change the determinant, we can rewrite this determinant by factoring out 9 from the second column. This effectively adds 8 times the original matrix to the second column without affecting the determinant calculation due to linearity of determinant calculations.