Learn German: Ich erkenne den Baum anhand des Blattes. - I recognize the tree on the basis of the leaf.

The word anhand is a preposition that requires the genitive case. It is used to point to evidence or clues. Since das Blatt (the leaf) is a neuter noun, its genitive form becomes des Blattes.

Why does Blattes get an -es ending instead of just -s?

Masculine and neuter nouns take an -s or -es ending in the genitive case. For short, one-syllable words like Blatt, the ending is usually -es simply because it makes the word easier to pronounce.

Could I use the preposition durch instead of anhand in this sentence?

You could say durch das Blatt (which would take the accusative case), but anhand is much more precise here. It specifically means 'on the basis of' or 'using this as a clue'. It perfectly captures that the leaf is the physical evidence you are using to identify the tree, whereas durch just means a general 'through' or 'by means of'.

Is anhand actually related to the noun Hand?

Yes, it historically comes from the phrase 'at the hand of'. You can think of it as having the evidence right in your hands to figure something out, which makes it very easy to remember the meaning of the word!