。
She asked me to pass her the salt.
Literal
She [topic-は] me [to-に] salt [object-を] take [for her-てくれる] [as-ように] asked.
A classic dinner-table moment encoded in grammar: 塩を取る ('take the salt') becomes 塩を取ってくれる ('take the salt for me') with the auxiliary ~てくれる, then is embedded under ~ように頼む as her request. Note that the くれる reflects 彼女's perspective in the original request — from her side, my passing the salt would be a favor done for her. The speaker preserves that perspective when reporting. Without the くれる, 取るように頼んだ would be a flat 'asked me to take/grab,' missing the favor framing.