That's a non-starter. Stepping away from the stove while there's oil on the heat is absolutely out of the question.
Literal
That [topic-は] can't-do consultation [copula-だな]. Oil-thing doing time [at-に], fire [gen-の] side [from-から] leave [nominalizer-のは] outrageous [copula-だ].
出来ない相談 '(a) request that cannot be granted' is an idiom for 'that's a non-starter / no deal.' 油物 'fried food' is compound noun for dishes being deep-fried or pan-fried in oil. 火の傍 '(the) side of the fire,' with 傍 (そば) 'side / next to' in its written kanji form. 言語道断 is a 四字熟語 literally '(beyond) the path of words,' meaning 'outrageous / inexcusable / beyond words' — used for shocking or unacceptable behavior.