If the outer side is \(s\) tiles, the top and bottom contribute \(2s\). The left and right sides contribute \(2(s-2)\) more, so the count is \(4s-4\).

For forty-four tiles, \(4s-4=44\), giving \(s=12\). Equivalently, add the four corners back, divide forty-eight by four, and obtain twelve.

Every frame count is a multiple of four. Forty-six is not, so no whole-number side length can use exactly forty-six tiles.

Answer

Forty-four tiles makes a frame with outer side length \(12\) tiles. Forty-six tiles is impossible.