He type of mutation represented below is a(n) the big red fly had one eye (wild type) the fbi gre dfl yha don eey (mutant)

Framshift mutation

Explanation:

The frame shift mutation is also known as reading frame shift or framing error mutation, during which an insertion or deletion occurs at a single position but it effects the sequence of whole gene in such a way that complete sequence is disturbed.

If we look at the sequence given in example:

Wild sequence: the big red fly had one eye

Mutant:               the fbi gre dfl yha don eey

An insertion mutation occured at the start of sequence big, where f got inserted. We know that a 3 set of nucleotides called codon is transcribed and translated into single amino acid of protein. So when f got added it disturbed the frame and all the sequences of next codons got altered.

In short the ehole protein will have wrong sequence of amino acid and it is worst type of mutation that badly effects an organism.

Hope it help!