Dear student,
(PtCL4)2- has square planar geometry  because it has 4 bonds and 2 lone  pairs of electrons. Pt is one of those strange elements  like S and P  that has 6 regions of high electron density.  Look at it like this: Draw  Pt in the center, and put 4 Cl around it. Now each Cl comes in with 7  electrons and Pt comes in with 6. Because there is a -2 charge you add  two more electrons. So now you have each Cl bonded to Pt with a single  bond which means 2 electrons. Now you have 4 extra electrons which means  2 lone pairs.
 

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