Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 21

$t=-1$ or $t= 3/2$.

Using the definition of the absolute value, we have $$ |1-4t|+8=13\Longrightarrow |1-4t|=13-8=5\\ \Longrightarrow 1-4t=5~or~ 1-4t=-5 .$$ Thus, we solve the two possible equations: $4t=-4~or~4t=6$ and hence $t=-1$ or $t=6/4=3/2$.