Identify your use: sipping/mockingtail (needs liqueur-style sweetness) or baking (needs nut aroma without breaking the recipe).
Choose the closest match from the list (hazelnut liqueur for most recipes; syrup+vanilla if you need lower alcohol).
Use the listed ratio; for syrup/extract swaps, start with slightly less than the original amount and add up after the first taste.
For baking, dissolve syrup/extract fully in the wet ingredients before mixing the dry ingredients.
Taste-check: if the result tastes flat, add a small pinch of salt or a tiny splash of vanilla to round nut notes.