#### Answer

The inflection point is at $t=2$.
Concave up on $t\in (2, \infty)$
Concave down on $t\in (-\infty, -2)$.

#### Work Step by Step

We have
$$y=t^3-6t^2+4, \quad y'=3t^2-12t, \quad y''=6t-12$$
The inflection point is when $y''=6t-12=0$, that is $t=2$.
Concave up when $y''\gt 0$, which occurs at $t\in (2, \infty)$
Concave down when $y''\lt 0$, which occurs at $t\in (-\infty, -2)$.