Solution:

The orbital speed \( v \) of a satellite is given by:

\[
v = \sqrt{\frac{GM}{r}}
\]

where \( r \) is the radius of the orbit.

Let the speeds of satellites A and B be \( v_A \) and \( v_B \), and their orbital radii be \( 4R \) and \( R \), respectively. Using the relation:

\[
v_A = \sqrt{\frac{GM}{4R}}, \quad v_B = \sqrt{\frac{GM}{R}}
\]

Given \( v_A = 3v \), we can write:

\[
3v = \sqrt{\frac{GM}{4R}}
\]

Now, the speed of satellite B is:

\[
v_B = \sqrt{\frac{GM}{R}} = 2 \times \sqrt{\frac{GM}{4R}} = 2 \times 3v = 6v
\]

So, the speed of satellite B is \( 6v \).