I think you're having trouble in your block diagram reduction. I (ironically) don't actually have the control system toolbox, but consider the following maths:
Your starting equation:
$$
\boxed{K_p + K_ds}\rightarrow \boxed{\frac{1}{\left(s+6\right)\left(s+12\right)}}
$$
You can "rephrase" your $K_p$ as $\left(K_p\left(\frac{\frac{1}{K_p}}{\frac{1}{K_p}}\right)\right)$, which reduces to $\frac{1}{\frac{1}{K_p}}$.
It looks almost like instead of multiplying the denominator by $\frac{1}{K_p}$ that you're instead just adding $K_p$ to the denominator. Then I think that things are further complicated by not distributing; it looks like you're applying the $K_p$ term to your plant, then taking that result and multiplying that by the $K_d$ term.
To put it a little clearer, it looks like you're doing something like:
$$
\boxed{A + B}\rightarrow\boxed{C}\\
\boxed{B}\rightarrow\boxed{AC}\\
\boxed{BAC}\\
$$
when the right answer should actually be the distributed:
$$
\boxed{A+B}\rightarrow\boxed{C}\\
\boxed{\left(A+B\right)\left(C\right)} \\
\boxed{AC + BC}\\
$$
So, starting out with rephrasing the proportional gain:
$$
\boxed{\frac{1}{\frac{1}{K_p}} + K_ds}\rightarrow \boxed{\frac{1}{\left(s+6\right)\left(s+12\right)}} \\
$$
Then distribute the terms:
$$
\boxed{\left(\frac{1}{\frac{1}{K_p}} + K_d s\right) \left(\frac{1}{\left(s+6\right)\left(s+12\right)} \right)} \\
$$
(I'll drop the boxes from here)
$$
\frac{1}{\frac{1}{K_p}}\left(\frac{1}{\left(s+6\right)\left(s+12\right)} \right) + K_d s \left(\frac{1}{\left(s+6\right)\left(s+12\right)}\right) \\
$$
Notice here that the left term is modifying the denominator, but the right term isn't. You need common denominators to add numerators, so you'll have to modify the right term by the same $\frac{\frac{1}{K_p}}{\frac{1}{K_p}}$:
$$
\frac{1}{\frac{1}{K_p}}\left(\frac{1}{\left(s+6\right)\left(s+12\right)} \right) + K_d s\left(\frac{\frac{1}{K_p}}{\frac{1}{K_p}}\right) \left(\frac{1}{\left(s+6\right)\left(s+12\right)}\right) \\
$$
Distribute the $K_d s$:
$$
\frac{1}{\frac{1}{K_p}}\left(\frac{1}{\left(s+6\right)\left(s+12\right)} \right) + \left(\frac{K_d s\frac{1}{K_p}}{\frac{1}{K_p}}\right) \left(\frac{1}{\left(s+6\right)\left(s+12\right)}\right) \\
$$
A crude cleanup now to combine terms:
$$
\frac{1}{\frac{1}{K_p}}\left(\frac{1}{\left(s+6\right)\left(s+12\right)} \right) + \left(\frac{\frac{K_d}{K_p}s}{\frac{1}{K_p}}\right) \left(\frac{1}{\left(s+6\right)\left(s+12\right)}\right) \\
$$
$$
\frac{1}{\frac{1}{K_p}\left(s+6\right)\left(s+12\right)} + \frac{\frac{K_d}{K_p}s}{\frac{1}{K_p}\left(s+6\right)\left(s+12\right)} \\
$$
$$
\frac{1+\frac{K_d}{K_p}s}{\frac{1}{K_p}\left(s+6\right)\left(s+12\right)} \\
$$
Now you have it in a non-standard form because the $s$ in the numerator has a coefficient that's not $1$, so get it to one by:
$$
\left(\frac{\frac{K_p}{K_d}}{\frac{K_p}{K_d}}\right)\left(\frac{1+\frac{K_d}{K_p}s}{\frac{1}{K_p}\left(s+6\right)\left(s+12\right)}\right) \\
$$
Then that reduces to:
$$
\frac{s+\frac{K_p}{K_d}}{\frac{1}{K_d}\left(s+6\right)\left(s+12\right)} \\
$$
I compared step results from your original and the above and they're similar, but not quite exactly the same. As I mentioned, I can't use the tf
functions, etc. in Matlab, but hopefully this helps you out!