I hear that his current work is very busy. [Syntax]

The correct answer is "が". This sentence uses the pattern "~そうです" (I hear that ~) to report what someone said or heard. The reported content is "今(いま)の仕事(しごと)がとても忙(いそが)しい" (his current work is very busy). Within this embedded clause, "今(いま)の仕事(しごと)" (current work) is the subject of the i-adjective "忙(いそが)しい" (busy). The subject of an adjective is marked by the particle "が". "今(いま)の" modifies "仕事(しごと)", and "仕事(しごと)" is the subject noun, both already present. "とても忙(いそが)しい" is the predicate, which comes after the subject and particle.

正解は「が」です。「〜そうです」は伝聞を表す表現です。伝聞の内容は「今の仕事がとても忙しい」で、「今の仕事」が形容詞「忙しい」の主語であるため、主格助詞の「が」が必要です。「今の」と「仕事」はすでに文中にあり、「とても忙しい」は「仕事が」の後ろにくる述語のため不適当です。