You did not mention what should be unique to each row in the output. I assumed it should be AppId. Given that, the trick is the Partition By where you rank each row for each grouping of AppId. What you seek is a crosstab. Given that you said there can be up to four rows for each group, we can build a static crosstab from that. 
;With RnkItems As
    (
    Select GID, AppId, GName, GDesig, GBusinessName
        , Row_Number() Over ( Partition By AppId Order By GID, GName ) As Rnk
    From SourceData
    )
Select AppId
    , Min( Case When Rnk = 1 Then GName End ) As GName1
    , Min( Case When Rnk = 1 Then GDesig End ) As GDesig1
    , Min( Case When Rnk = 1 Then GBusinessName End ) As GBusinessName1
    , Min( Case When Rnk = 2 Then GName End ) As GName2
    , Min( Case When Rnk = 2 Then GDesig End ) As GDesig2
    , Min( Case When Rnk = 2 Then GBusinessName End ) As GBusinessName2
    , Min( Case When Rnk = 3 Then GName End ) As GName3
    , Min( Case When Rnk = 3 Then GDesig End ) As GDesig3
    , Min( Case When Rnk = 3 Then GBusinessName End ) As GBusinessName3
    , Min( Case When Rnk = 4 Then GName End ) As GName4
    , Min( Case When Rnk = 4 Then GDesig End ) As GDesig4
    , Min( Case When Rnk = 4 Then GBusinessName End ) As GBusinessName4
From RnkItems
Group By AppId
SQL Fiddle version