Hello, jadee!
Your explanation is confusing.
I think I've translated it . . .
We have a point A(4,10).
and four horizonal lines: .$\displaystyle \begin{array}{cc}L1: & y = 10 \\ L2: & y = 8 \\ L3: & y = 4 \\ L4: & y= 2 \end{array}$
Find points $\displaystyle B,C,D$ on $\displaystyle L_2, L_3, L_4$ so that $\displaystyle ABCD$ is a rhombus. Code:
 (4,10)
10+     o          
 * A *
 * * B
8+   *       o (b,8) 
 * *
 D * *
4+  o       *     
 (d,4) * *
 * C *
2+        o       
 (c,2)

+

We must determine $\displaystyle b,c,d$ so that: .$\displaystyle \overline{AB} \,=\, \overline{BC} \,=\,\overline{CD} \,=\,\overline{DA}.$
Am I close?