Diferent between like and desire?

[Bruce Mee]

English Language Tests, Intermediate level

ESL/EFL Test #98 "Student Teacher Dialogue", question 9

Teacher: Well, if you ........., I could give you lessons next week.

(a) love
(b) like
(c) would
(d) desire

English Language Tests, Intermediate level

ESL/EFL Test #98 "Student Teacher Dialogue", answer 9

Teacher: Well, if you like, I could give you lessons next week.

Correct answer: (b) like
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what is the diferent between like and desire?

[Daniela]

DESIRE means to have a strong longing for, to covet, to wish. It is much stronger than like. Usually we desire something which is difficult or impossible to get, for example “desire peace”.
LIKE expresses a preference.
If you like, we can meet you there.

Success! :)

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[English Teacher]

Hi,
Doesn't this sentence discuss the conditional type 2?
Because we can see the second part of this clause have " could"
And so isn't the answer must be " would " as the past tense of the main verb " will"?
Thank you for revealing the answer.
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