I am using taxonomy menu module but I want to change the taxonomy path from taxonomy/term/tid to subject/term title.


You need to use Path auto module .. Alias taxonomy term paths...

The Pathauto module automatically generates URL/path aliases for various kinds of content (nodes, taxonomy terms, users) without requiring the user to manually specify the path alias. This allows you to have URL aliases like /category/my-node-title instead of /node/123. The aliases are based upon a "pattern" system that uses tokens which the administrator can change.

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