Answer
The relative speed of approach of one particle with respect to the other is $~~0.95 c$
Work Step by Step
Let $u'$ be the speed of the particle approaching the north pole.
Then $u' = 0.80c$
Let $v$ be the speed of the Earth reference frame relative to the particle approaching the south pole.
Then $v = 0.60c$
We can find $u$:
$u = \frac{u'+v}{1+u'~v/c^2}$
$u = \frac{0.80c+0.60c}{1+(0.80c)(0.60c)/c^2}$
$u = 0.95 c$
The relative speed of approach of one particle with respect to the other is $~~0.95 c$
