Compare the product of the two triangle numbers with the product of the square and circle numbers in each group. One is always exactly double the other.
Rather than jumping straight to a formula, it helps to first rule out the simpler relationships, like addition, before landing on multiplication.
Try addition first: in Group 1, $t_1 + t_2 = 6 + 8 = 14$, while $s + c = 8 + 12 = 20$. In Group 2, $t_1+t_2 = 5+6=11$, while $s+c=10+6=16$. The gap is 6 in the first case and 5 in the second, so a simple addition rule does not hold across both groups.
Try the ratio of the triangle product to the square: in Group 1, $t_1 t_2 / s = 48/8 = 6$, and the circle is 12, exactly twice that. In Group 2, $t_1 t_2 / s = 30/10 = 3$, and the circle is 6, again exactly twice that.
State the rule: the circle always equals twice the product of the two triangles, divided by the square, that is $c = \dfrac{2 t_1 t_2}{s}$.
Applying this to Group 3, where $t_1 = 3$, $t_2 = 12$, and $s = 4$: $c = \dfrac{2 \times 3 \times 12}{4} = \dfrac{72}{4} = 18$.
Let's summarize:
Addition does not give a consistent rule across the three groups.
The circle equals twice the triangle product divided by the square, in every group.
So the number that replaces the question mark is 18.
