To find the value of $k$ in the expression $f(x) + k$, we need to express it in terms of the given function $f(x) = 2x + 4$.

Here’s how to approach this:

1. Start with the function $f(x) = 2x + 4$.
2. The expression $f(x) + k$ means adding some constant $k$ to $f(x)$.

Since no specific value of $f(x) + k$ is given, $k$ could be any real number, depending on the context. Therefore, without additional information, we can only state that $k$ is an arbitrary constant added to the function $f(x)$.

Would you like further details or do you have any specific context to narrow down the problem?

Here are some questions to explore:

1. What happens to the graph of $f(x)$ when $k$ changes?
2. How does $k$ affect the intercept of the function $f(x)$?
3. Can $k$ be determined if we know a specific output of the function $f(x) + k$?
4. How does the domain and range of $f(x)$ change with the addition of $k$?
5. What is the effect of adding $k$ on the slope of the function?

Tip: Adding a constant $k$ to a function shifts the graph of the function vertically without changing its slope.