Answer
$\vec{r}_{(2)} = (6\hat{i} - 106\hat{j})\,m$
Work Step by Step
We're given:
$\vec{r}_{(2)} = (2t^3-5t)\hat{i} + (6-7t^4)\hat{j}$, where $\vec{r}(t)$ is in meters.
We can plug in $t=2\,s$ to obtain:
$\vec{r}_{(2)} = ((2*2^3-5*2)\hat{i} + (6-7*2^4)\hat{j})\,m$
$\vec{r}_{(2)} = (6\hat{i} - 106\hat{j})\,m$.
