find the nominal rate of interest convertible quarterly which is equivalent to a nominal rate of discount of 6% p.a. convertible monthly

Answer 1

Is the "discount" confusing you ?

I believe most textbooks would handle it like this:
Let the annual discount rate be i
1-i = (1 - .005)^12 = .995^12 = .94162
i = .058377 or a discount of 5.8377%

Had it been just plain old interest .....

let the nominal rate be i
(1+i) = (1.005)^12
1+i = 1.06168
i = .06168
the nominal annual rate is 6.168%

check on the method your text or your notes uses, or your teacher showed you