Answer
$A\subseteq B$ is false.
$A\subset B$ is false.
Work Step by Step
Represented using the roster method, the sets look like this:
$A=\{4, 5, 6, 7, 8, 9\}$
$B=\{2, 3, 4, 5, 6, 7, 8\}$
We can see that.
$A\subseteq B$ is false, as there is at least one element in set $A$ ($9$) that is not an element in set $B$.
$A\subset B$ is false, as $A\subseteq B$ is false.