DURATION converts a series of numbers into a Duration value. If your values to be summed are already durations, DURATION is unnecessary, and should be dropped.
SUMIFS requires 1 + 2n arguments, where n is the number of conditions that must be met.
=SUMIFS(sum-values,test-values,condition,test-values,condition)
The first argument is the range of cells containing the values to be summed.
The second and third (and each pair after that) are the range of cells containing the test-values, then the condition that those values must meet.
With respect to syntax, your formula, shown here with returns entered to separate the elements, looks correct.
=
SUMIFS(
Andreas::Table 1::L;
Andreas :: Table 1 :: H;">="&$C$2;
Andreas :: Table 1 :: J;"<="&$D$2;
Andreas::Table 1::D;"="&B4
)
(Note: The last condition is revised in my example)
Column L: This column should contain the values to be summed. These should be Duration values.
Column H contains the starting date for (the section of) the project recorded on a row. The condition states this date must be equal to or later than the date in cell C2 of the table containing the formula.
Column J contains the end date for (the section of) the project recorded on a row. The condition states this date must be equal to or later than the date in cell D2 of the table containing the formula.
Column D contains the name of (the section of) the project recorded on a row. The condition states this text must match the text in cell B4 of the table containing the formula.
Here's my sample data table, which contains data only in the columns used in the formula:

Here is the table containing the formula (and the results):

Formula, placed in B2 and filled down
=SUMIFS(Table 1::L,Table 1 :: H,">="&$C$2,Table 1 :: J,"<="&$D$2,Table 1::D,"="&A)
Duration values were set to provide an easy check of how many projects have been summed on each project (one for each of projects one, two, four and five, two for project three, and none for lines six, seven, eight and nine).
Three rows were not summed:
Row 1 (project four): Starting date before January 1, 2013
Row 9 (Project one): End date after January 31, 2013
Roow 10 (Project two): End date after January 31, 2013
Note: As There is only one Table 1 included in the document, the Sheet name (Andreas) was dropped from the formula by Numbers. With "Table 2" renamed as "Table 1, Numbers automatically revised the formula to include th Sheet name:
=SUMIFS(Andreas::Table 1::L,Andreas::Table 1 :: H,">="&$C$2,Andreas::Table 1 :: J,"<="&$D$2,Andreas::Table 1::D,"="&A)
Regards,
Barry