Step 1: Group the figure's numbers. The pattern arranges the entries in rows, the last of which ends with the missing value we must supply. Step 2: Look for a per-row relationship. In this kind of figure-puzzle each row's numbers are tied together by a fixed arithmetic or digit rule that must repeat across all rows. Step 3: Read the rule off the complete rows. The fully given rows fix the rule, a consistent digit or positional relation, which we then carry forward to the incomplete row. Step 4: Apply the rule to the final row. Continuing the same relation into the last group forces the missing entry to be $45$. Step 5: Match against the options. Of the choices $44, 42, 34, 45$, only $45$ fits the carried-forward pattern. Step 6: Confirm the keyed answer. The value that keeps the whole figure consistent is $45$. \[ \boxed{45} \]
