Find the real solutions of the equation. \[ |3-4 t|+3=18 \]

Step 1 ：First, we need to solve the equation |3-4t|+3=18. The absolute value function splits the equation into two cases. One where the expression inside the absolute value is positive and one where it is negative.

Step 2 ：For the case where the expression inside the absolute value is positive, we have the equation 3-4t+3=18. Solving this equation gives us the solution t=-3.

Step 3 ：For the case where the expression inside the absolute value is negative, we have the equation -(3-4t)+3=18. Solving this equation gives us the solution t=\(\frac{9}{2}\).

Step 4 ：We have two potential solutions, t=-3 and t=\(\frac{9}{2}\). We need to check these solutions in the original equation to make sure they are valid.

Step 5 ：Substituting t=-3 into the original equation, we find that the equation holds true. Therefore, t=-3 is a valid solution.

Step 6 ：Substituting t=\(\frac{9}{2}\) into the original equation, we find that the equation holds true. Therefore, t=\(\frac{9}{2}\) is a valid solution.

Step 7 ：Final Answer: The real solutions of the equation are \(\boxed{-3}\) and \(\boxed{\frac{9}{2}}\).