Although this would be an appropriate question for a Language forum, and not exactly Hinduism persay, the word meaning is as follows.
The word Abhyahanyata, as you said is prefixed with Abhi, which means "moving towards".
The other part of the word is Ahanyanta, which is a word in past tense plural third person, and derives from the root √han, which means, "To kill or to strike." This comes from the explanation of the verb root as
- "Han Himsaagatyoh"
"Han" is used for Himsaa, violence, and Gati, movement.
In a broader sense of meaning, this root would refer to violent actions or movements, which are applied to killing and striking respectively.
Over here, Ahanyanta therefore would mean, "They struck (the conchshells, bugles, trumpets, drums and horns)." Adding the prefix Abhi (moving towards) implies that the striking of drums and other instruments was an aimed action, thus implying that the signal for the battle call had been given by the army commanders, and the troops were to start assembling in their respective formations.
We can see that this battle call is given by Bhishma in the previous verse,
तस्य सञ्जनयन्हर्षं कुरुवृद्धः पितामहः ।
सिंहनादं विनद्योच्चैः शङ्खं दध्मौ प्रतापवान् ॥ १२ ॥
Then Bhīṣma, the great valiant grandsire of the Kuru dynasty, the grandfather of the fighters, blew his conchshell very loudly, making a sound like the roar of a lion, giving Duryodhana joy. (BG.1.12).
This is when the Pandavas respond by blowing their conches, and Arjuna and proceeds with Krsna to the centre of the battlefield, to observe the army formations on both sides, and begin the discourse that is Bhagavad-Gita.
Reference: Dhaturupa Manjari