Transition level is the lowest flight level with 1013 mb set on the pressure altimeter.
In the question, the pressure on the day is 970 mb which is 43 mb lower than standard 1013. The question asks you to assume a pressure difference of 1 mb per 30 feet, hence:
43 x 30 = 1290 feet. This is by the way the transition layer.
3000 feet transition altitude + transition layer of 1290 feet = 4290 feet.
The lowest flight level which can be used on the day is therefore FL45.
The second part of the questions asks you for the correct flight level according to quadrantal rule.
You will be flying a heading of 260 which will therefore be a postive flight level. The first positive flight level will be FL60.
Your answer is A: FL45 Transition Altitude and FL60 Flight Level.
Hope that helps.