In this phrase, notice particularly the use of the "symbol for repeat" (ๆ ไม้ยมก). Literally the speaker says "slowslow" (ช้าช้า), but this is written, not as "slow" + "slow" (i.e. not ช้าช้า), but rather as "slow" + "symbol for repeat" (i.e. ช้าๆ).
Summary
The Thai translation for “Speak slowly.” is พูดช้าๆด้วย. The Thai, พูดช้าๆด้วย, can be broken down into 3 parts:"to speak" (พูด), "very slow; slowly" (ช้าๆ) and "too; also" (ด้วย).