hopefully this helps!
Let's think of this number as T|U where T is the tens position digit and U is the units position digit.
Original number has value 10T+U. U=3T (first sentence).
Second sentence deals with U|T, which has value ('new number') 10U+T.
Half the new number is 21 < twice the original means:
½(10U+T) = 2(10T+U) - 21
There you have a system of two equations in two unknowns. You may now solve it.
Check the answers for reasonableness and correctness. (Also check my work producing the last equation)
Note I have used the vertical separation symbol "|" to segregate the two digits of a 2-digit number.