Answer :

AL2006

Ah hah !  I work with these things all the time, so I can read it straight
off the picture.  However, I realize that you probably don't, and can't ...
otherwise you wouldn't need to look for help online.  So I'll try to
explain through it:

-- This is a "topographic map", and those brown lines on it are
"elevation contours". 

-- All of the points on one brown line are all at the same elevation
(altitude, height, etc.), so if you follow one of the brown lines wherever
it goes, you're following a level path.

-- The little numbers somewhere on each brown line tell you the elevation
(above something) of all the points on that line.  You can see lines that
are 35-ft, 45-ft, 50-ft etc.  above whatever the reference is for this map. 

If a line has no numbers on it, then it's halfway between the next lower
line and the next higher line.  There's a line on this map with no number
on it between 35 and 45 ... the elevation of every point on this line is 40.
There's another one between 45 and 50 with no number on it ... every
point on that line must be at elevation of 47.5 .

-- On this kind of map ...

==> The flattest ground is where the lines are far apart, like where
that lake is.  That's where there's a big distance between the 25-ft
line on one side, to the 30-ft line on the other side.  All of the land
between those 2 lines is within 5 feet of the same height.
Same for the land between the 30-ft line and the 35-ft line ... every
point between those 2 lines is within 5 feet of the same height.  It's
a very level place.
The gentlest 'shallowest' slope is always on the path that crosses the
fewest lines, or where the lines you have to cross are the farthest apart. 
That's how we'll find the answer to the question, in just a moment.

==>  The steepest slope is where the lines are close together, like
from 35-ft to 45-ft to 50-ft.  In that short distance, the land rises 15-ft
because it's going up the steep side of Mount Cleveland.

==>  You can also see where the peaks are, like where the 52-ft line
makes a circle.  The peak of the mountain is inside that circle, and from
there, no matter which way you walk from the peak, the land goes down.


-- The absolutely shallowest path to the peak of the mountain would start
on the left side of the map, about 1/3 of the way up from the bottom. 
There seems to be 2 lines there, but if you follow them up and around,
you find that they're both the same 50-ft line.  So from that point on the
edge, all the way to the peak of the mountain, the land only rises a
little more than 2 feet.  But you'd still have to get yourself up to that
starting point, and this path is not one of the choices.

-- If you start at the bottom center just below the end of the lake, OR
if you start from the lower right in Arthur Park, OR if you start at the
upper right in the marsh and swamp up at that end of lake, heading
for the peak of the mountain from any one of those points, you start
from elevation lower than 30 feet, and your hike is flat and pretty level
for a while, until it gets to the 35-ft line.  And then, suddenly, it goes
ZUP ... 17 feet straight up to the top, in a short distance from there,
and crossing lines that are close together.

-- If you start from the bottom left corner, that point is already at an
elevation of about 45-ft, so it only has about 7-ft more to rise from there
to the peak. ALSO ... Starting from there, and going all the way to the
peak, the path goes roughly the same way the brown lines go ... it's
roughly parallel to them ... so there's more distance from one line to
the next one.

So "bottom left" is the place to start.

Note:
The numbers on the lines of a real topographic map are much more
likely to be marked in meters, not feet, so everything I've just described
would be 3.28 times as hard to climb.