Answer: <4, 6>
The rule is that <a, b> is perpendicular to <b, -a>. You swap the coordinates and then change the sign of one of the coordinates.
In this case, a = -6 and b = 4
<a, b> = <-6 , 4>
<b, -a> = <4, 6>
Compute the dot product of the two vectors
<-6, 4> dot <4, 6> = (-6)(4) + (4)(6) = -24 + 24 = 0
Since the dot product is 0, this confirms that <4,6> is perpendicular to the given vector.
note: any scale factor of <4,6> will work as well. For example, <8, 12> is another possible answer since you multiply both parts of the answer above by the value 2. So there are infinitely many answers in the form <4*k, 6*k> where k is any real number.