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In SUMIF, all ranges should be equal. So, second parameter of B4 should also be B4:B16 assuming B4:B16 contain dates.
But SUMIFS will not support a formula inside it.
=SUMPRODUCT(J32:J44 * (L32:L44="Jan") *(TEXT(Budget!B4:B16,"mmm") ="Jan"))
But if you are looking that only B4 should be equal to Jan, then B4 can't be part of SUMIF.
Probably, you are looking for a formula of this kind
=SUMIFS(J32:J44,L32:L44,"Jan") * (TEXT(Budget!B4, "MMM) = "Jan")