Solve the linear equation:
$\dfrac{{3t - 2}}{4} - \dfrac{{2t + 3}}{3} = \dfrac{2}{3} - t$

Hint: Here, we have to find the value of t by solving the given linear equation using mathematical operations.

Complete step-by-step answer:
Given Linear equation is
$\dfrac{{3t - 2}}{4} - \dfrac{{2t + 3}}{3} = \dfrac{2}{3} - t$
Now we have to find the value of (t)
We can find the value of t by solving the given linear equation i.e.
$\dfrac{{3t - 2}}{4} - \dfrac{{2t + 3}}{3} = \dfrac{2}{3} - t$

Also we can write the above equation in the following form i.e.
\[
  \Rightarrow \dfrac{{3(3t - 2) - 4(2t + 3)}}{{12}} = \dfrac{2}{3} - t \\
  \Rightarrow \dfrac{{(9t - 6) - (8t + 12)}}{{12}} = \dfrac{2}{3} - t \\
  \Rightarrow \dfrac{{9t - 6 - 8t - 12}}{{12}} = \dfrac{2}{3} - t \\
  \Rightarrow \dfrac{{t - 18}}{{12}} = \dfrac{2}{3} - t \\
  \Rightarrow t {\text{ - 18}} = 12(\dfrac{2}{3} - t) \\
  \Rightarrow t {\text{ - 18}} = 8 - 12t \\
  \Rightarrow 13t = 26 \\
  \Rightarrow t = 2 \\
 \]
Thus, the value of t is 2.

Note: These types of questions can be solved by simplifying the linear equation. Here in this question we have solved the given linear equation and found the value of t.