I don’t see how you can be asked to solve this unless you have studied modular arithmetic. Here is one simplification you should be able to understand. Let’s say that z is the number we are looking for. z = 58x + 32y. The advantage of expressing z like this is that it breaks the problem down into two smaller problems. Since 32y is divisible by 32, the remainder of z when divided by 32 is the same as the remainder of 58x when divided by 32. Similarly, the remainder of z when divided by 58 is the remainder of 32y when divided by 58.
Therefore we want to find x such that 58x has a remainder of 30 when divided by 32 and
we want to find y such that 32y has a remainder of 44 when divided by 58.
I found a trick for finding x. Unfortunately, I don’f know of an easy way to find y.
Part 1. Find x such that 58x has a remainder of 30 when divided by 32. 58x = 32x + 26x, so we want to find x such that 26x has a remainder of 30. Here is where the modular arithmetic comes in. 26 = -6 mod 32. Since (-5)x(-6)=30, x = -5 = 27 mod 32. If you do the arithmetic, you will see that in fact 58×27 has a remainder of 30 when dividing by 32.
Part 2. Find y such that 32y has a remainder of 44 when divided by 58. I know a way of finding y, but it is a bit complicated.