Stored Procedure doesn't show result in SQL Server
You need to split your parameters into rows and use where ... in as a check.

Using a split function like this one your code could look like this.

CREATE PROCEDURE [dbo].[sp_tst_CSENG_JulieCapitalHours]
    @StartDate DATETIME ,
    @EndDate DATETIME ,
    @ProjHomeGrp NVARCHAR(MAX) ,
    @ProjHier NVARCHAR(MAX)
AS 
BEGIN

    DECLARE @ProjHomeGrpTbl TABLE (Value NVARCHAR(4))

    INSERT INTO @ProjHomeGrpTbl(Value)
    SELECT LTRIM(RTRIM(s))
    FROM dbo.Split(',', @ProjHomeGrp);

    DECLARE @ProjHierTbl TABLE (Value NVARCHAR(5))

    INSERT INTO @ProjHierTbl(Value)
    SELECT LTRIM(RTRIM(s))
    FROM dbo.Split(',', @ProjHier);

    SELECT  [Capital Project] ,
            [Capital Task] ,
            ResourceName ,
            ProjectName ,
            [Project Home Group] ,
            ActualWork ,
            TimeByDay ,
            ResourceStandardRate ,
            ActualWork * ResourceStandardRate AS Dollars ,
            [Project Hierarchy]
    FROM    [IR.CapOnly]
    WHERE   ( TimeByDay &gt;= @StartDate )
            AND ( [Project Home Group] in (SELECT Value FROM @ProjHomeGrpTbl) )
            AND ( TimeByDay &lt;= @EndDate )
            AND ( ActualWork &gt; 0 )
            AND ( [Project Hierarchy] in (SELECT Value FROM @ProjHierTbl) )
    ORDER BY ProjectName ,
            ResourceName

END