How to determine the empirical formula for terephthalic acid from its combustion products?
You are on the right track, but if you google terephthalic acid, you will know that your formula is not correct. 

One mistake you are making is using the final mass of the $\ce{CaCl2}$ and $\ce{NaOH}$ and not the change in mass. For example, let's take the $\ce{CaCl2}$:

First, we don't know what the initial mass of $\ce{CaCl2}$ is, so we cannot calculate the final mass the way you are trying to do. We are only given the mass of the terephthalic acid (0.4953 g). The calcium chloride and sodium hydroxide are not part of this mass. 

However, we know that the calcium chloride increased in mass by 0.1613 g, presumably by absorbing water (you are correct that the calcium chloride is absorbing water). So, the mass of water produced by the combustion reaction is 0.1613 g.

Similarly, we only know the change in mass of the sodium hydroxide (1.0495 g), which occurred by absorbing carbon dioxide. So the mass of carbon dioxide is 1.4095 g.

The second mistake is to assume that all of the mass of the carbon dioxide and water produced must come from the original mass of the terephthalic acid. Not so! We have excess oxygen added contributing mass to the reactant side, and this oxygen is also in the products. 
$$\ce{C}_x\ce{ H}_y\ce{ O}_z\ce{ +}\left(\frac{4x+2y-z}{4}\right)\ce{ O2 -&gt; }x\ce{CO2 +}\frac{y}{2}\ce{ H2O}$$

We need to do more maths to figure out how much of the leftover mass in the original sample is oxygen. Here is the beginning of the setup, now that you have some sense of the mass of water and carbon dioxide produced:


Mass of water produced $\ce{-&gt;}$ moles of water produced $\ce{-&gt;}$ moles of hydrogen in the water produced (and in the original sample!) $\ce{-&gt;}$ grams of hydrogen (in sample) 
Mass of carbon dioxide produced $\ce{-&gt;}$ mass of carbon (in sample)
Mass of oxygen in sample (by subtraction) $\ce{-&gt;}$ moles of oxygen in sample 


You are doing everything correctly after this.