Maria S. gave a good explanation. I would add the following details though:

If you move numbers from one side to another, you have to change its sign. In your question, we have 4x - 102 + 63. -102 is going to become positive, and +63 is going to be negative. Therefore:

4x = 102 - 63

You can do 102 - 63 by hand if you find the mental math a bit too difficult here.

I'd also like to add that you want 4x to become x on its own (since we want an answer of x = something). In algebra, when a number and a letter are beside each other, like 4x, that actually means 4 times x. Now, to get rid of the 4, we need to do its opposite. The opposite of multiplying is dividing, so we're going to divide 4x divided by 4. The two 4s will cancel out, leaving only x on the left side.

Finally, if we did something to the left side, we are forced to do it to the right side as well. So, you must divide 39 by 4. Dividing and fractions are actually the same thing, so 39 divided by 4 can be written as 39/4. Since 39/4 cannot be simplified, you can leave it written that way on the right side. Therefore,

x = 39/4

If you want a decimal answer, if you did 39 divided by 4 by hand, you'd get 9.75. Both of these are the correct answer.

(Note: You'll get some questions that actually tell you what form they want the answer in. So, if they told you to write your answer to a specific number of decimal places, make sure you use the decimal answer, and also round it to the correct number of decimal places.

If you have any further questions, don't hesitate to contact me.