To find the value of $t$, we need to solve the given algebraic equation:

$ \frac{(2t+1)}{3t} + \frac{(3t-2)}{4t} = 2 $

Steps to Solve the Equation

1. Combine Fractions: Find the least common multiple (LCM) of the denominators $3t$ and $4t$, which is $12t$. Rewrite each fraction with the common denominator: $ \frac{4 \times (2t+1)}{4 \times 3t} + \frac{3 \times (3t-2)}{3 \times 4t} = 2 $ $ \frac{8t+4}{12t} + \frac{9t-6}{12t} = 2 $
2. Simplify the Numerator: Add the numerators together over the common denominator: $ \frac{(8t+4) + (9t-6)}{12t} = 2 $ $ \frac{17t - 2}{12t} = 2 $
3. Eliminate Denominator: Multiply both sides of the equation by $12t$ (assuming $t \neq 0$): $ 17t - 2 = 2 \times (12t) $ $ 17t - 2 = 24t $
4. Isolate $t$: Rearrange the terms to solve for $t$. Subtract $17t$ from both sides: $ -2 = 24t - 17t $ $ -2 = 7t $
5. Calculate the Value of $t$: Divide by 7: $ t = \frac{-2}{7} $

The calculated value is $ t = -\frac{2}{7} $. Note that this value is not among the options provided (A: $\frac{12}{5}$, B: $-\frac{7}{5}$, C: $\frac{6}{5}$, D: $-\frac{8}{5}$). Based on the standard mathematical procedure, the solution is $t = -\frac{2}{7}$.