If you travel #4# miles in one direction, turn left, travel #6# miles, turn right and travel #4# miles, then how far will you be from the starting point?

I'm not entirely clear what you are asking for, but let me address the problem you describe:

Starting from the origin #(0,0)# travel a distance of #4# units.

Let us choose to travel in the positive direction along the #x# axis. That will take us to the point #(4,0)#.

Turning to the left will orient us in a positive direction parallel to the #y# axis.

Moving forward #6# units will add #6# to the #y# coordinate, taking us to the point #(4,6)#.

Turning to the right will orient us in a positive direction parallel to the #x# axis.

Moving forward #4# units will add #4# to the #x# coordinate,
taking us to the point #(8,6)#

If we drop a perpendicular onto the #x# axis from this final point we get the point #(8,0)#.

The points #(0,0)#, #(8,0)# and #(8,6)# are the vertices of a right angled triangle. The distance from the origin #(0, 0)# to the point #(8,6)# is the length of the hypotenuse of this triangle, so is equal to the positive square root of the sum of the squares of the lengths of the other two sides.

#8^2 + 6^2 = 64 + 36 = 100 = 10^2#

So the distance between the start and finish points is #10# miles.