please check my answer(one with star). The solubility of borax is directly proportional to temperature. Therefore, the sign of H is

A. negative*
B. positive
C. unknown with the given information

since solubility shifts the reaction to the right, therefore it is exothermic so H has to be negative. Am i right?

If I write the equation this way, I see

borax(solid) + heat + water ==> borax(solution)(aq) which says that as we add heat to the left side more borax dissolves (and that agrees with the statement in the problem). Does that make it exothermic?
(Your statement that "solubility shifts the reaction to the right" should read, I think, to "heat shifts th reaction to the right". It isn't the solubility that is shifting anything; it's the added heat that is making it more soluble.

since heat is added, so does that mean H is positive(endothermic)

Yes, you are correct! The solubility of borax (sodium borate) is indeed directly proportional to temperature. As temperature increases, the solubility of borax also increases.

Regarding the sign of enthalpy (ΔH) for the dissolution of borax, your reasoning is accurate. When a substance dissolves in water, the process can be either endothermic (absorbs heat) or exothermic (releases heat). In the case of borax, since solubility increases with temperature, we can conclude that the dissolution process is exothermic.

Therefore, the correct answer would be A. negative*, indicating that the sign of ΔH for the dissolution of borax is negative.