I’m trying to SUM multiple columns of every rows that match a criteria.

I’ve a table with the time planned of multiple people over several tasks over the years:

In another table in the same file(let’s admit in the same sheet), I’m trying to say, for every months, what is the time planned for every task, no matter the user, for the current month and the following ones.

Typically, for the cell for “January – Task 1”, I would like to have 2+4+4+5+2+5 = 22
But for the same task, in July, I only expect to have 4+5+2+5 = 16, in august only 5+2+5=12, …

When several people worked on the same task, their time should be also summed up.

I could, manually, for each task, summing the July->December for all the rows I know are assigned to this task, but there is a lot of tasks, I might add a task to some people, …
I would like, for each task to automatically search for all the assignement.

I tried to assemble some “SUMIF”, but I didn’t managed to have something working.
I could see some way to make it work, by adding a column after each month that provide the sum of the next ones, but in my real case, I’ve 36 months, and that makes a lot of columns and noise.