Create a flow diagram and describe it using the rule: Multiply by 2, then add 3. Also, determine the rule for an input-output diagram and write a number sentence.

Let's test a rule of the form (Input $\times A$) + B.
Using the first two pairs:
$9A + B = 32$
$6A + B = 23$
Subtracting the second equation from the first:
$(9A + B) - (6A + B) = 32 - 23$
$3A = 9$
$A = 3$
Substitute $A=3$ into $6A + B = 23$:
$6(3) + B = 23$
$18 + B = 23$
$B = 5$
The rule is (Input $\times 3$) + 5.

The first operation box is $\boxed{\times 3}$.
The second operation box is $\boxed{+ 5}$.

Let's test a rule of the form (Input $\times A$) + B.
Using the first two pairs:
$7A + B = 62$
$5A + B = 46$
Subtracting the second equation from the first:
$(7A + B) - (5A + B) = 62 - 46$
$2A = 16$
$A = 8$
Substitute $A=8$ into $5A + B = 46$:
$5(8) + B = 46$
$40 + B = 46$
$B = 6$
The rule is (Input $\times 8$) + 6.

The first operation box is $\boxed{\times 8}$.
The second operation box is $\boxed{+ 6}$.