$3 t^{2}+2 t^{2}=6^{2}$

Step 1 ：Simplify the equation $3 t^{2}+2 t^{2}=6^{2}$ to $5t^{2} = 36$

Step 2 ：Divide both sides of the equation by $5$ to get $t^{2} = 7.2$

Step 3 ：Take the square root of both sides to solve for $t$, $t = \sqrt{7.2}$

Step 4 ：Calculate the square root of $7.2$ to get the final answer

Step 5 ：Final Answer: \(\boxed{2.6832815729997477}\)