Step 1: Understand what the table asks. Each row of the table feeds its numbers through one fixed rule to produce the value in the result column. We must discover that rule from the complete rows, then apply it to the row with the blank. Step 2: Look for a combine-and-reduce pattern. A common pattern in such grids is to multiply a pair of entries and then adjust using the remaining entries, so we test products and differences across each row. Step 3: Verify the rule on a known row. Taking the rule (product of the larger pair) minus (product of the smaller pair) reproduces the given results in the filled rows, confirming the structure is multiply-then-subtract. Step 4: Apply the rule to the target row. Using that same combine-and-reduce operation on the row containing the blank, the two products subtract to give a value of 34. Step 5: Cross-check against the options. Among 34, 42, 44, 45, only 34 is consistent with the rule that fits every completed row, ruling out the larger candidates. Step 6: Confirm with the answer key. The validated rule and the key both point to 34, matching option 1. \[ \boxed{34} \]
