Understanding IEEE 754 floating-point specification requires some time and effort. You should read your textbook or lecture notes, or at least Wikipedia pages about floating point and single-precision floating-point format. The fact that Java implements IEEE 754 as well as parameters of single-precision floating-point (the size of the significand and exponent) are stated in the Oracle documentation.
First you need to convert 176.2058 to binary: 10110000.00110100101011110100111100001100...2. Next you round it to 24 bits: 10110000.0011010010101111. In the final representation, the decimal point should be after the first bit: 1.01100000011010010101111 * 27. The exponent is stored as the sum of 7 (or whatever it is for a given number) and 127, i.e., 134 in this case. In binary, 134 = 100001102. The first bit of significand is always 1, so it is not recorded, which leaves 23 bits. The final representation consists of the sign bit (0 means +1), the exponent and the significand. Thus, it is
0 10000110 01100000011010010101111.
Here are a couple of online calculators that can compute floating-point representation.