I'm not an expert on this, but see the section of the PROC GLM documentation on "Multiple Comparisons." You can choose from about a dozen different multiple comparison adjustments. In particular, read the "Recommendations" and "Interpretation of Multiple Comparisons" sections at the end of the doc.
The main graphical presenation of multiple comparisons is the Hsu diffogram, which is created by default when you have ODS GRAPHICS ON and request multiple comparisons. (Or you can request it with PLOTS=DIFFOGRAM on the MEAN or LSMEANS statement.)
For example, examine the output of
ods graphics on;
proc glm data=sashelp.cars;
class type;
model mpg_city = type;
lsmeans type / adjust=tukey;
run;
For a discussion about how to interpret a diffogram and why many researchers prefer it over the graph that you pasted into your question, see High (2011) "Interpreting the Differences Among LSMEANS in Generalized Linear Models"
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