Step 1: Recall alkylation of amines.
Amines undergo successive alkylation with alkyl halides. In presence of excess alkyl halide, exhaustive alkylation occurs.
Step 2: Apply to ethylamine.
Ethylamine reacts repeatedly with ethyl iodide forming secondary, tertiary amines and finally a quaternary ammonium salt.
Step 3: Final product formation.
With large excess of ethyl iodide, the reaction proceeds to form tetraethyl ammonium iodide.
Step 4: Conclusion.
The final product is tetraethyl ammonium iodide.