6.NS.C.7 math practice. Learn by doing.

First compute the difference: $11 - 10 = 1$. Then take the absolute value: $|1| = 1$.

The interval is open: $-\dfrac{19}{4} = -4.75$ and $\dfrac{11}{2} = 5.5$, so values must satisfy $-4.75 < x < 5.5$. Check each choice: $-5 < -4.75$ (outside), $-4$ is between the bounds, $\dfrac{11}{2}$ equals the upper endpoint (not strict), and $-\dfrac{19}{4}$ equals the lower endpoint (not strict).

Absolute value gives the non-negative distance from $0$, so $|-2| = 2$.

Compare positions: $\dfrac{9}{5} = 1.8$, $-\dfrac{2}{3} \approx -0.67$, $\dfrac{5}{8} = 0.625$, and $-\dfrac{7}{12} \approx -0.58$. The greatest is $\dfrac{9}{5}$.

The absolute value of a non-negative number is itself: $|8| = 8$.

Distance from zero is absolute value: $\left|-\dfrac{23}{8}\right| = \dfrac{23}{8}$.

$0$ is its own distance from $0$, so $|0| = 0$.

Convert the bounds: $-\dfrac{83}{7} \approx -11.86$ and $\dfrac{67}{4} = 16.75$. Strictly between means integers $n$ with $-\dfrac{83}{7} < n < \dfrac{67}{4}$, so $n$ runs from $-11$ through $16$, including $0$. Count with $16 - (-11) + 1$: subtracting endpoints gives the gap between them; the $+1$ counts both $-11$ and $16$ inclusive.