To solve the absolute value inequality $|5x - 6| \leq 4$, start by isolating the absolute value expression, which in this case is already isolated. Next, translate the inequality into the equivalent compound inequality $-4 \leq 5x - 6 \leq 4$. Solve this compound inequality by adding $6$ to all three parts, resulting in $2 \leq 5x \leq 10$. Then, divide each part by $5$ to isolate $x$, which gives $\frac{2}{5} \leq x \leq 2$. On a number line, this solution is graphed by placing closed circles at $\frac{2}{5}$ and $2$, and shading the segment between them to indicate all included values. In interval notation, this contiguous solution set is written as $[\frac{2}{5}, 2]$.