To solve this problem, we need to determine the number of ATP and NADPH$_2$ molecules required for the synthesis of one molecule of glucose during the Calvin cycle.$\newline$The Calvin cycle, also known as the C$_3$ cycle, involves three main stages: carboxylation, reduction, and regeneration.$\newline \bullet$Carboxylation:$\newline$ - In this stage, CO$_2$ is fixed into a 5-carbon sugar, ribulose bisphosphate (RuBP), to form two molecules of 3-phosphoglycerate (3-PGA).$\newline \bullet$Reduction:$\newline$ - Each molecule of 3-PGA is phosphorylated by ATP and then reduced by NADPH$_2$ to form glyceraldehyde-3-phosphate (G3P).$\newline$ - For every CO$_2$ molecule fixed, 2 ATP and 2 NADPH$_2$ are used.$\newline \bullet$Regeneration:$\newline$ - Some of the G3P molecules are used to regenerate RuBP, which requires additional ATP.$\newline$ - For every 3 CO$_2$ molecules fixed, 5 G3P molecules are used to regenerate 3 RuBP, consuming 3 ATP.$\newline$To synthesize one molecule of glucose (C$_6$H$_{12}$O$_6$), 6 CO$_2$ molecules need to be fixed.$\newline \bullet$Total ATP and NADPH$_2$ required:$\newline$ - For 6 CO$_2$ molecules, the reduction stage requires 12 ATP and 12 NADPH$_2$ (2 ATP and 2 NADPH$_2$ per CO$_2$).$\newline$ - The regeneration stage requires an additional 6 ATP (3 ATP per 3 CO$_2$).$\newline$ - Therefore, the total ATP required is 18 (12 for reduction + 6 for regeneration), and the total NADPH$_2$ required is 12.$\newline$Thus, the correct answer is Option 2: 18 ATP and 12 NADPH$_2$.