1. Given data

• Masses: $m_1 = M$, $m_2 = 5M$
• Radii: $R$ and $2R$
• Initial distance between centers: $12R$

They move only due to mutual gravitational attraction.

2. Condition for collision

Just before collision, the two spheres touch each other. So the distance between their centers becomes

$R + 2R = 3R$

Hence, the total decrease in separation is

$12R - 3R = 9R$

3. Use center of mass concept

Since only internal forces act, the center of mass remains fixed. Therefore, the distances moved by the two bodies are inversely proportional to their masses:

$m_1 x_1 = m_2 x_2$

Let the smaller body move distance $x_1$ and the larger body move distance $x_2$. Then

$M x_1 = 5M x_2$

$x_1 = 5x_2$

Also, total closing distance is

$x_1 + x_2 = 9R$

Substitute $x_1 = 5x_2$:

$5x_2 + x_2 = 9R$

$6x_2 = 9R$

$x_2 = 1.5R$

Thus,

$x_1 = 5(1.5R) = 7.5R$

4. Final answer

The smaller body covers

$\boxed{7.5R}$

So the correct option is C.