This/That – ce (m) or cet (m) if vowel or h follows, cette (f) even when vowel follows
(Pronounced Se, Set and Set)
To remember that This/That is pronounced se, set and set (ce, cet and cette) in French, use the following mnemonic:
This, sir, (ce) is the set (cet) of golf clubs you should replace that old set (cette) of yours with.

NOTE:
The French use the same word for the pronouns of "this" and "that". However, which word they use depends on whether the noun it refers to is masculine or feminine. If the noun is feminine then they use the word cette. If the word is masculine they use the word ce, unless the masculine noun begins with a vowel or silent h, in which case they use the word cet.
Examples of ce, cet and cette (this/that) in a sentence
Ce livre est très intéressant.
(This/That book is very interesting.)
Cet hôtel est assez cher.
(This/That hotel is quite expensive.)
Cette femme est mon professeur.
(This/That woman is my teacher.)