To find the missing base length of the rectangular pyramid, we can start with the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times B \times h \]
Where:
- \( V \) is the volume,
- \( B \) is the area of the base,
- \( h \) is the height.
From the information given, we know:
- The height \( h = 6 \) mi,
- The volume \( V = 154 \) mi³.
- The base of the right face (which we assume corresponds to one dimension of the base rectangle) is \( 7 \) mi.
Let the unknown dimension of the base be labeled as \( b \) mi. The area of the base \( B \) would be the product of the two dimensions:
\[ B = 7 , \text{mi} \times b , \text{mi} \]
Plugging this into the volume formula, we have:
\[ 154 = \frac{1}{3} \times (7b) \times 6 \]
Simplifying, we can first calculate the constant terms:
\[ 154 = \frac{1}{3} \times 7 \times 6 \times b \] \[ 154 = \frac{42b}{3} \] \[ 154 = 14b \]
Now, we solve for \( b \):
\[ b = \frac{154}{14} = 11 \]
Thus, the missing measure of the base of the front face is \( \boxed{11} \) mi.