Answer : The average beta of the new stocks be to achieve the target required rate of return =1.76

Working notes for the above answer is as under

mutual fund manager has a $40 million portfolio with a beta of 1.00.

The risk-free rate is 4.25%,

The market risk premium is 6.00%.

The manager expects to receive an additional $60 million which she plans to invest in additional stocks. expected return to be 13.00%.

Bi = 1
rf = 4.25%
rm = 6%

Using CAPM You are already given the market risk premium as 6%, this is telling you that the return of the market over the risk free rate is 6%, ie the term (Rm-RFR) =6%,
Using CAPM, a portfolio return of 13% requires a total portfolio beta of:

13=4.25+B(6)
B(6) = 13 – 4.25
B(6) = 8.75
B= 1.458

The Beta of the total portfolio must be 1.458 to give a return of 13%.

To determine the average beta of just the new stocks (as requested):

.4(1)+0.6(B)=1.458

0.6b=1.058

b=1.76