The following parametric equations trace out a loop.

$x(t)=12-\frac{3}{2}{t}^2$

$y(t)=-\frac{3}{6}{t}^3+3t+3$

Note that the curve is symmetric about the line $y=3.$

a$.$ Find the $t-$values at which the curve intersects itself. $($Separate multiple values by commas.$)$

$t=$

b$.$ What is the total area inside the loop?

Area: