Your work appears to be correct.
The results from a graphing calculator are in agreement.
Given:
The equation of line is

To find:
The x and y-intercept of the given line.
Solution:
We have,

Putting x=0, we get

Add 6 on both sides.


Divide both sides by 4.

So, the y-intercept is
.
Putting y=0 in given equation, we get

Add 5 on both sides.


Divide both sides by 7.

So, the x-intercept is
.
You could rewrite

as

and be tempted to cancel out the factors of

. But this cancellation is only valid when

.
When

, you end up with the indeterminate form

, which is why

is not a zero.
Comparing map distance to real distance we get 2cm/4km. That means 1cm = 2km.
So the map distance is half the real distance (well, technically not as one is in cm and the other in km but it’s enough to think this way) and a real distance of 10km must mean a map distance of half that (again ignoring the units) so we get 5cm.