How does the splitting in this molecule take place?
According to given data, you may consider expected peak patterns are not complicated such as $\mathrm{ABX}$ or $\mathrm{A_2B}$  patterns (more reading look here. This is simply a  $\mathrm{A_2X}$  pattern ($\delta_X = \pu{6 ppm}$ and $\delta_A = \pu{1 ppm}$ without geminal coupling of two $\ce{H_b}$ protons), and hence, peak is a $dt$ for $\ce{H_b}$ as depicted below with relative heights of the peaks:



Similarly, $\ce{H_c}$ is also a $dt$ resonance with $J = 1 \text{ &amp; } \pu{8 Hz}$ and $\ce{H_a}$ is a $tt$ with $J = 1 \text{ &amp; } \pu{5 Hz}$. OP should able to figure out the intensities of relevant peaks. 

A valuable reference:

Roy H. Bible, Jr., Ph.D., In Interpretation of NMR Spectra: An Empirical Approach; Springer Science: New York, NY, 1965 (https://doi.org/10.1007/978-1-4684-8288-1) (Note: Most relavent to this question is chapter 4 of the book titled "Higher-Order Spin Patterns and Multiple Resonance").