To solve this problem, let's break it down into two steps based on the transformations:

Step 1: Apply the translation

The translation rule is: $(x, y) \to (x + 1, y - 4)$

The coordinates of $Z$ are $(1, 3)$. Applying the translation rule to $Z(1, 3)$:

$Z' = (1 + 1, 3 - 4) = (2, -1)$

Step 2: Apply the reflection across the y-axis

Reflection across the y-axis changes the x-coordinate by changing its sign, while the y-coordinate remains the same. So, for the point $Z'(2, -1)$, the reflected point $Z''$ will have coordinates:

$Z'' = (-2, -1)$

Final Answer:

The location of $Z''$ is $(-2, -1)$.

Thus, the correct option is: $\boxed{(-2, -1)}$

Would you like further details on any of these steps, or is there another question you'd like to explore?

Here are some related questions you could try:

1. What is the new location of point X after the same transformations?
2. How would the coordinates of the points change if the reflection was across the x-axis instead?
3. What is the general formula for a translation of the form $(x, y) \to (x + a, y + b)$?
4. How does reflecting a point over the y-axis affect its distance from the origin?
5. What would the coordinates of triangle XYZ be if the translation was different, such as $(x, y) \to (x - 2, y + 3)$?

Tip: When applying transformations, breaking down each step and working with the coordinates individually can help avoid errors, especially when dealing with multiple transformations like translations and reflections.