Working backwards
$\times 4 \rightarrow -30\rightarrow \times2 \rightarrow -10\rightarrow$ answer 2 digits
$\div4\leftarrow +30 \leftarrow \div2 \leftarrow + 10 \leftarrow$ answer 2 digits
Answer 2 digits, largest possible $99$
Answer
$+10$
$\div2$
$+30$
$\div4$
$99$
$109$
$54.5$
$84.5$
Not an integer
$98$
$198$
$54$
$84$
$21$ good
So the largest possible choice is 21.
Using algebra
Brian chooses be $b$
Multiply by $4$ and subtract $30$: $4b-30$
multiply this by $2$ and subtract $10$: $2(4b-30)-10 = 8b-70$
Answer two digits, largest possible $99$
If Brian got $99$:
$8b-70=99\\
\Rightarrow 8b=169\\
\Rightarrow b = 21.125$
So $b\le21.125$ and $b$ is an integer so $b=21$