Suzuki uses the JIS (Japanese Industrial Standard) sizes, which can differ from the common European Metric sizes.
See the chart at: Common Metric Thread Pitches, JIS
[Note that JIS 8mm usually has a 1.25 thread pitch, not the 1.0 that's shown in the chart. I think it's an errror.]
Determine (measure) the bolt diameter, you'll know which thread you need.
JIS standard fasteners have REDUCED hex bolt and nut sizes, so go by the bolt diameter, not the wrench size.
6 x 1mm bolt = 10mm wrench (across the flats)
8 x 1.25mm bolt = 12mm wrench
10 x 1.25 = 14mm wrench
I prefer to stick with JIS sizes, so as not to have to carry additional wrenches.
Suzuki lug nuts are 12mm x 1.25, (19mm across flats) whereas some other Japanese cars use 12 x 1.50 lugnuts.