Here we want to find what is the remainder of $n\cdot a$ when dividing by $8$ for $n=1,2,\dots,7$ and $a = 5,6$. For example, for $n = 3$ and $a=5$, we have $3\cdot 5 = 15$, which is $7 \pmod{8}$, and for $n = 7$ and $a = 5$, we have $7 \cdot 5 = 35$, which is $3 \pmod{8}$.

The purpose of this problem is to see how the set of different values $\pmod{8}$ that can be obtained by multiplying the possible remainders $\pmod{8}$ (so $n=0,1,\dots,7$) by $5$ and $6$ differ from one another.