Whether you can marry your first cousin twice removed depends in part on the laws of the place where you propose to have the marriage performed. In most of the US, you can marry your first cousin, so marrying your first cousin twice removed would also be permitted.
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The child of your first cousin, once removed, is your first cousin, twice removed, if your first cousin once removed is the child of your first cousin. If your first cousin once removed in the first cousin of one of your parents, the child is your second cousin.
Your parent's first cousin is your first cousin, once removed. Your parent's first cousin, once removed is your first cousin, twice removed. Your parent's second cousin is your second cousin, once removed. Your parent's second cousin, once removed is your second cousin, twice removed.
Your first cousin's grandchild is your first cousin, twice removed.
The child of your first cousin oncer removed is your first cousin twice removed, or your second cousin, depending on which end of the relations you are on..
Your great grandfather's nephew was your grandfather's first cousin. You are two generations removed from your grandfather and his cousin. Therefore you and your great grandfather's nephew are first cousins, twice removed.