#### Answer

$t=\dfrac{106}{27}$

#### Work Step by Step

Raising both sides to the fourth power results to
\begin{array}{l}\require{cancel}
3(4-t)^{1/4}=6^{1/4}
\\\\
\left( 3(4-t)^{1/4} \right)^4=\left( 6^{1/4} \right)^4
\\\\
81(4-t)=6
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
81(4-t)=6
\\\\
81(4)+81(-t)=6
\\\\
324-81t=6
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
324-81t=6
\\\\
-81t=6-324
\\\\
-81t=-318
\\\\
t=\dfrac{-318}{-81}
\\\\
t=\dfrac{106}{27}
.\end{array}
Upon checking, $
t=\dfrac{106}{27}
$ satisfies the original equation.