This means $FGH$ has perimeter $6+8+10 = 24\text{cm}$.
Consider the line $IJ$. The triangle $HIJ$ is similar to the triangle $HGF$. This is because $HJ = \frac 12 HF$, $HI = \frac 12 HG$ and $\angle JHI = \angle FHG$. This means $JI = \frac 12 FG = 4\text{cm}$.
Similarly, $JK = \frac 12 HG$ and $IK = \frac 12 FH$, so the perimeter of $IJK$ is half that of $FGH$. This means that $IJK$ has a perimeter of $12 \text{cm}$.