What you need to know about perpendicular lines is that they have the negative reciprocal slope of the line they are perpendicular to. What this means is that you take the first line's slope, add a negative sign, and switch the numerator and denominator, and that's the slope of the perpendicular line!
In this question, y=2x-1 is our original line. Using the formula y=mx+b, where "m" is the slope, we can see that our "m" in this case is 2. So, negate 2. It becomes -2. Then, switch numerator and denominator. -2 is really -2/1, so let's make it -1/2. That's the slope of the perpendicular line.
Now, we have to make it pass through (-2,6). So right now, all we have is a line like this: y=-1/2x
If we plug in the x-coordinate of our desired point, -2, we get y=-1/2(-2), so y=1. But wait, isn't y supposed to equal 6, since that's the y-coordinate we were given? Yes! So all you need to do is get from 1 to 6, which we can do by adding 5!
So the new equation is y=-1/2x+5!