Will I be taxed if a transfer shares of a mutual fund to another fund within the same brokerage

When you make this "transfer" from one fund to another you are actually selling shares in the first fund and using the proceeds to buy shares in the second fund. In a regular taxable account you will have to report the sale of the first fund, and if you made a gain on the sale you pay capital gains tax on it. If you have a loss on the sale you can use that loss to offset other gains you may have, and if you don't have other gains you can take a deduction on the loss of up to $3K and then roll any additional loss amount to use in a future year against future gains.