$3 is indeed half-way between $2 and $4, which on your zero-centered scale (if you are zero-centering based on the increments of $2, $4, $6, and $8) is now half-way between -3 and -1, or -2. So, you would use -2 to multiply by the coefficient to compute the part-worth utility for $3.
But, if prior to running the utility estimation you scanned all the prices shown to respondents, including the $3, to create your zero-centering transform, then that array would have been the prices ($2, $3, $4, $6, and $8). The zero-centered prices would have been coded for utility estimation as -2.6, -1.6, -0.6, 1.4, and 3.4. If you had coded your design matrix for utility estimation using that transform, then now to calculate the price at $3 you should multiply -1.6 times the coefficient.
Just be consistent with whatever transformation you used during utility estimation.